Geometry Unit 10 Answers PHS
(L1) The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.
Thrm. 10.1
(L3) The three expressions, sin-1, cos-1, and tan-1 are called _____ trig functions and are used to find the measure of the acute angles of a right triangle if you know the lengths of at least two sides.
inverse
(Q2) The three expressions, sin⁻¹, cos⁻¹, and tan⁻¹ are called _____ trigonometric functions.
inverse
(LAB10.1) Find the probability of a student getting a geometry slip and a second student getting an algebra slip.
34/96
(LAB10.1) Choose 3 desserts from a menu of 6.
(3)(2)(1)=6
(LAB10.1) Choose 3 favorite desserts in order from 1st to 3rd from a menu of 6.
(6)(5)(4)/(3)(2)(1)=20
(L2) _____ is a trigonometric ratio consisting of the length of the side adjacent to a given acute angle of a right triangle to the length of the hypotenuse.
Cosine
(L2) _____ is a trigonometric ratio consisting of the length of the side adjacent to a given acute angle of a right triangle to the length of side opposite the given angle; the reciprocal of the tangent.
Cotangent
(LAB10.1) Volleyball players are randomly placed on teams by spinning a spinner with four congruent, colored sections. They are assigned positions on the team by rolling a six-sided die. The team colors are red, black, green, and purple.What is the conditional probability of rolling a 5 given that the spinner landed on black?
1/24
(LAB10.1) Find the probability of Ysedria selecting a dog, giving it to a friend, and then selecting another dog.
11/59
(LAB10.1) Since this situation requires the elimination of all redundant arrangements, by which number would the total number of possible arrangements be divided?
12
(L1) If h=6 in; y=18 in then find x.
2 in
(Q1) x=1.5 cm; y=5.5 cm; Find h .
2.9 cm
(LAB10.1) How many possible ways can 4 Team Jet members be chosen to win the prizes?
210
(L2) Find tan D. (right triangle; dimensions: 3 cm, 4 cm, 5 cm)
3/4
(L2) Find cos F. (right triangle; dimensions: 3 cm, 4 cm, 5 cm)
3/5
(L2) Find sin D. (right triangle; dimensions: 3 cm, 4 cm, 5 cm)
3/5
(Q1) Use the value s₂=6.2 Find tan L
3/6.2≈0.5
(Q1) Use the value s₂=6.2 Find cos J
3/7≈0.4
(Q1) Use the value s₂=6.2 Find sin L
3/7≈0.4
(LAB10.1) How many possible ways can 4 Team ATV members be chosen to win the prizes?
30
(L1) If c=10 cm; x=1.6 cm; find s₁.
4 cm
(L1) If x=2 cm; y=8 cm then find the length of the altitude h.
4 cm
(L2) Find tan F. (right triangle; dimensions: 3 cm, 4 cm, 5 cm)
4/3
(L2) Find cos D. (right triangle; dimensions: 3 cm, 4 cm, 5 cm)
4/5
(L2) Find sin F. (right triangle; dimensions: 3 cm, 4 cm, 5 cm)
4/5
(LAB10.1) Exactly 8 cards were taken from a standard deck of cards: 2 hearts, 2 clubs, 2 spades, and 2 diamonds. A card is drawn from the 8 cards, and then a second card is drawn without replacement.Find the conditional probability of getting a heart on the first draw and then getting a club on the second draw without replacement.
4/7
(L1) Given: ΔABC is a right triangle with altitude BD¯ Prove: ΔABC~ΔCDB~ΔADB
Reasons- 3: Def. of Altitude 5: 6: 7: Reflexive 8: 9: Transitive
(Q1) c=7 cm; y=5.5 cm; Find s₂.
6.2 cm
(Q1) Use the value s₂=6.2 Find tan J
6.2/3≈2.1
(Q1) Use the value s₂=6.2 Find cos L.
6.2/7≈0.9
(LAB10.1) Of all the students at a high school, 54% are in band and play sports. 78% of all students at the high school play sports. Find the probability that a student is in band given that the student plays sports. Round your answer to the nearest tenth.
69.2%
(LAB10.1) Of the students in a class, 2/3 mastered the final exam and passed the course; 7/8 of the students mastered the final exam. What is the probability that a student passed the course given the student mastered the final exam? Round your answer to the nearest tenth percent.
76.2%
(L1) If c=10 cm; y=8.4 cm; find s₂.
9.17 cm
(LAB10.1) A bag contains 20 marbles. 15 of them are red and 5 of them are green in color. Find the probability of picking a green marble. A. What is the number of favorable outcomes each time when picking a marble? B. How many choices or members are in the sample space? C. Calculate the probability: P=number of favorable outcomes in the event/members in the sample space=
A bag contains 20 marbles. 15 of them are red and 5 of them are green in color. Find the probability of picking a green marble. A: 5 (E) B: 20 (B) C: ¼ (D)
(L1) Find the arithmetic mean and geometric mean of the set of numbers. {2, 18}
Arithmetic mean: 10 Geometric mean: √36 or 6
(Q1) Find the arithmetic mean and geometric mean of the set of numbers. {3, 17}
Arithmetic mean: 10 Geometric mean: √51
(L1) Find the arithmetic mean and geometric mean of the set of numbers. {2, 32}
Arithmetic mean: 17 Geometric mean: √64 or 8
(Q1) Find the arithmetic mean and geometric mean of the set of numbers. {3, 7}
Arithmetic mean: 5 Geometric mean: √21
(L1) The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.
Cor. 1 of Thrm. 10.1
(L1) The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg.
Cor. 2 of Thrm. 10.1
(L3) Find the measure of ∠A. 1. Determine the information that is given and what you are trying to find. Given: a. length of side opposite = __________ b. length of side adjacent = __________ Find: m∠A 2. Choose the correct inverse trig ratio. __________ 3. Substitute the given information. __________ 4. Solve the problem. __________
Find the measure of ∠A. 1. Determine the information that is given and what you are trying to find. Given: a. length of side opposite = E b. length of side adjacent = I Find: m∠A 2. Choose the correct inverse trig ratio. J 3. Substitute the given information. D 4. Solve the problem. F
(L2) _____ is a trigonometric ratio consisting of the length of the hypotenuse to the length of the side opposite a given angle of a right triangle; the reciprocal of the sine.
Cosecant
(L4) Determine the information that is given and what you are trying to find. Given: a. angle of depression b. vertical distance = 500 ft Find: horizontal distance 2. Choose the correct trig ratio. 3. Solve for the unknown. 4. Substitute the given information. 5. Solve the problem.
Determine the information that is given and what you are trying to find. Given: a. angle of depression D b. vertical distance = 500 ft Find: horizontal distance 2. Choose the correct trig ratio. J 3. Solve for the unknown. B 4. Substitute the given information. E 5. Solve the problem. F
(L4) Determine the information that is given and what you are trying to find. Given: a. angle of elevation b. horizontal distance Find: height x 2. Choose the correct trig ratio. 3. Solve for the unknown. 4. Substitute the given information. 5. Solve the problem.
Determine the information that is given and what you are trying to find. Given: a. angle of elevation K b. horizontal distance J Find: height x 2. Choose the correct trig ratio. D 3. Solve for the unknown. I 4. Substitute the given information. B 5. Solve the problem. [H]
(Q2) Find the measure of ∠B. (60/100)
Determine the information that is given and what you are trying to find. Given: a. length of side adjacent = A b. length of hypotenuse = J Find: ∠B 2. Choose the correct inverse trig ratio. I 3. Substitute the given information. D 4. Solve the problem. G
(Q2) Use the values sin45°=0.707, cos45°=0.707 ,tan45°=1 (83/100)
Determine the information that is given and what you are trying to find. Given: a. m∠A= B b. length of b= H Find: hypotenuse (c) 2. Choose the correct trig ratio. K 3. Solve for the unknown. J 4. Substitute the given information. C 5. Solve the problem. F
(Q2) The astronaut wants to make a vertical landing. He sees his landing spot at an angle of depression of 30º while 600 feet above the surface. How far must he move horizontally to make a vertical landing on that location? Use the values sin30°=0.5,cos30°=0.866,tan30°=0.577 (83/100)
Determine the information that is given and what you are trying to find. Given: a. m∠B= D b. length of b= K Find: adjacent (a) 2. Choose the correct trig ratio. F 3. Solve for the unknown. A 4. Substitute the given information. E 5. Solve the problem. B
(LAB10.1) Exactly 8 cards were taken from a standard deck of cards: 2 hearts, 2 clubs, 2 spades, and 2 diamonds. A card is drawn from the 8 cards, and then a second card is drawn without replacement.Which of the following statements is true?
Drawing a card from the deck and then drawing a second card without replacement are dependent events because the outcome of the first event affects the outcome of the second event.
(LAB10.1) Find the probability of flipping a coin and it coming up heads. A. What is the number of favorable outcomes each time when flipping the coin? B. How many choices or members are in the sample space? C. Calculate the probability: P=number of favorable outcomes in the event/members in the sample space=
Find the probability of flipping a coin and it coming up heads. A: 1 (G) B: 2 (E) C: ½ (C)
(LAB10.1) _____ probability is a type of probability that is determined by geometric measures, such as lengths, areas, or volumes.
Geometric
(L1) Greek mathematician and teacher who lived in the 2nd century B.C.
Hipparchus
(LAB10.1) If you are throwing a dart at a triangular target containing a square and are equally likely to hit any point on the target, what is the geometric probability that you will hit the small square? A. What is the area of the square? cm² B. What is the area of the triangle? cm² C. Calculate the probability: P=area of the square/area of the triangle=
If you are throwing a dart at a triangular target containing a square and are equally likely to hit any point on the target, what is the geometric probability that you will hit the small square? A: 4 (B) B: 10 (A) C: ⅖ (E)
(L3) Which statement is NOT correct?
If you know the measure of all three angles of a right triangle, you can find the length of each of the three sides.
(LAB10.1) In the box below, complete the remaining three rows of the list that models how to calculate the number of possible ways 4 team members can be selected to win the prizes. 1) F G H I J K L Let Lui win the 1st prize, so select L. 2) _________ _____________________________ 3) _________ _____________________________ 4) _________ _____________________________
In the box below, complete the remaining three rows of the list that models how to calculate the number of possible ways 4 team members can be selected to win the prizes. 1) F G H I J K L Let Lui win the 1st prize, so select L. 2) _________ _____________________________ 3) _________ _____________________________ 4) _________ _____________________________
(LAB10.1) _____ is the measure of how likely an event will occur .
Probability
(L2) _____ is a trigonometric ratio consisting of the length of the hypotenuse to the length of the side adjacent to a given angle of a right triangle; the reciprocal of the cosine.
Secant
(LAB10.1) Volleyball players are randomly placed on teams by spinning a spinner with four congruent, colored sections. They are assigned positions on the team by rolling a six-sided die. The team colors are red, black, green, and purple. Which of the following is true?
Spinning the spinner and rolling the die to select teams and positions represent independent events because the outcome of the first event does not affect the outcome of the second event.
(L2) _____ is a trigonometric ratio consisting of the length of the side opposite a given acute angle of a right triangle to the length of the side adjacent to the given angle.
Tangent
(LAB10.1) _____ probability is the ratio of the number of outcomes in an event to the number of members in the sample space.
Theoretical
(LAB10.1) Which of the following statements is true? (figurines)
The events are dependent because not replacing the first figurine affects the probability of selecting the second figurine.
(LAB10.1) Which of the following statements is true? (math problems)
The events are independent because replacing the first slip does not affect the probability of selecting the second slip.
(LAB10.1) Which of the following is a true statement? (Team Jet)
The situation is a combination because the order in which the members are chosen does not matter.
(LAB10.1) Which of the following is a true statement? (Team ATV)
The situation is a permutation because the order in which the members are chosen matters.
(L2) _____ ratios are the ratios of the lengths of the two sides of a right triangle.
Trigonometric
(Q1) _____ is the branch of mathematics that deals with the relationships between the sides and angles of triangles.
Trigonometry
(L3) Use the values: sin30°=0.5; cos30°=0.866; tan30°=0.577 1. Determine the information that is given and what you are trying to find. Given: a. m∠A= __________ b. length of a= __________ Find: hypotenuse (c) 2. Choose the correct trig ratio. __________ 3. Solve for the unknown. __________ 4. Substitute the given information. __________ 5. Solve the problem. __________
Use the values: sin30°=0.5; cos30°=0.866; tan30°=0.577 1. Determine the information that is given and what you are trying to find. Given: a. m∠A= E b. length of a= I Find: hypotenuse (c) 2. Choose the correct trig ratio. [D] 3. Solve for the unknown. L 4. Substitute the given information. G 5. Solve the problem. J
(L3) Use the values: sin30°=0.5; cos30°=0.866; tan30°=0.577 1. Determine the information that is given and what you are trying to find. Given: a. m∠A=__________ b. length of a= __________ Find: adjacent (b) 2. Choose the correct trig ratio. __________ 3. Solve for the unknown. __________ 4. Substitute the given information. __________ 5. Solve the problem. __________
Use the values: sin30°=0.5; cos30°=0.866; tan30°=0.577 1. Determine the information that is given and what you are trying to find. Given: a. m∠A= H b. length of a= A Find: adjacent (b) 2. Choose the correct trig ratio. [B] 3. Solve for the unknown. L 4. Substitute the given information. G 5. Solve the problem. F
(LAB10.1) What is the geometric probability of choosing a point on AB¯ ? A. What is the length of AB¯ ? cm B. What is the length of AC¯ ? cm C. Calculate the probability: P=length of AB¯/length of AC¯=
What is the geometric probability of choosing a point on AB¯ ? A: 2 (A) B: 8 (C) C: ¼ (G)
(Q2) If you know the measure of two _____ and the length of one side of a triangle, you can find the measure of the other angle and the length of the other two sides.
[sides]
(Q1) The positive nth root of the product of n factors is the _____.
geometric mean
(L1) A(n) ___ is a device for measuring the amount of incline or tilt of an object or a surface.
inclinometer
(Q2) Angle of elevation is the angle formed by a horizontal line and a line of sight to a point _____ the horizon.
above
(L2) Match the trigonometric name with the correct ratio: cos
adjacent/hypotenuse
(L1) useful for finding the average of a set of values that are similar
arithmetic mean
(Q1) The _____ is useful for finding the average of a set of values that are similar.
arithmetic mean
(Q1) The _____ is a trigonometric ratio consisting of the length of the hypotenuse to the length of the side opposite a given angle of a right triangle.
cosecant
(Q1) Which trigonometric ratio is calculated by adjacent/hypotenuse?
cosine
(Q1) The _____ is a trigonometric ratio consisting of the length of the side adjacent to a given acute angle of a right triangle to the length of side opposite the given angle.
cotangent
(L4) Angle of _____ is the angle formed by a horizontal line and a line of sight to a point below the horizon.
depression
(L4) Angle of _____ is the angle formed by a horizontal line and line of sight to a point above the horizon.
elevation
(LAB10.1) Any set of outcomes is called a(n) _____.
event
(LAB10.1) An activity in which results are observed is called a(n) _____.
experiment
(L1) The ___ is the positive nth root of the product of n factors.
geometric mean
(Q1) The _____ is used to compare values that are proportional.
geometric mean
(L2) Match the trigonometric name with the correct ratio: tan
opposite/adjacent
(L2) Match the trigonometric name with the correct ratio: sin
opposite/hypotenuse
(LAB10.1) Each result of an experiment is a(n) _____.
outcome
(L2) One of a pair of values whose product is one is called a(n) _____; also called the multiplicative inverse.
reciprocal
(LAB10.1) The _____ is the set of all possible outcomes of an experiment.
sample space
(Q1) The reciprocal of the cosine is the _____.
secant
(L2) The _____ is a trigonometric ratio consisting of the length of the side opposite a given acute angle of a right triangle to the length of the hypotenuse.
sine
(Q1) Which trigonometric ratio is calculated by opposite/hypotenuse?
sine
(L3) The process known as _____ a triangle is used for calculating unknown side lengths or angle measures of a triangle if certain of the side lengths and/or angle measures are known.
solving
(Q1) Which trigonometric ratio is calculated by opposite/adjacent ?
tangent
(Q2) The process known as solving a _____ is used for calculating unknown side lengths or angle measures of a triangle if certain of the side lengths and/or angle measures are known.
triangle
(L1) used to compare values that are proportional
trig mean
(Q1) The ratios of the lengths of the two sides of a right triangle are called _____ ratios.
trigonometric
(L1) The branch of mathematics that deals with the relationships between the sides and the angles of triangles is called ___.
trigonometry
(Q2) If you know the lengths of _____ and the measure of one angle of a right triangle, you can find the measure of the other two angles and the length of the other side.
two sides
