goemetry B unit 10

6) 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

3) 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

8) ___ 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

6) ___ 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

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.

angles

Angle of depression is the angle formed by a horizontal line and a line of sight to a point _____ the horizon.

below

Find the arithmetic mean and geometric mean of the set of numbers.

c. 10 d. 20

Choose the law and the formula that would be used to solve the triangle.

c. Law of Cosines g. c2=a2+b2-2abcosC

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

4) The hot air balloon is 500 feet off the ground. The observer sees his landing zone at an angle of depression of 45°. Find the horizontal distance to his landing spot.

d. 45° b. adj=opp/tan j. tan=opp/adj e. adj=500tan45∘ h. 707 ft

Find the length of c . Use the values sin 45∘=0.707, cos 45∘=0.707 ,tan 45∘=1

d. 90° f. 7.07 cm j. hyp=adj/cosA f. 7.07 cm c. hyp=5cos45∘ l. 5.02 cm

1) Angle of ___ is the angle formed by a horizontal line and a line of sight to a point below the horizon.

depression

Choose the law and the formula that would be used to solve the triangle.

e. Law of Sines b. sinAa=sinCc

2) One of a pair of values whose product is one is called a(n) ___; also called the multiplicative inverse.

reciprocal

If you know the lengths of all three _____ of a right triangle, you can find the measures of each of the three angles.

sides

Which trigonometric ratio is calculated by opposite/hypotenuse

sin

3) 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

2) 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

9) Convert from degrees to radians. 270°= _____ rad

3π/2

The positive nth root of the product of n factors is the _____.

geometric mean

1) The positive acute angle formed by the terminal side of an angle in standard position and the x-axis is called a ___.

reference angle

13) Convert from radians to degrees. 1.5 rad = _____

85.9°

4) ___ 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

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

4) A ___ is a circle with a radius of one unit that has its center at the origin on the coordinate plane.

unit circle

Which trigonometric ratio is calculated by adjacent/hypotenuse

a. 21/2 c. 21

Choose the law and the formula that would be used to solve the triangle.

c. Law of Sines b. sinA/a=sinC/c

3) 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

5) A unit of angular measure equal to the length of the arc divided by the radius of the arc is a ___.

radian

A radian is a unit of angular measure equal to the length of the arc divided by the ___ of the arc.

radius

The reciprocal of the cosine is the ___.

secant

2) An angle with its vertex at the origin and one of its rays on the x-axis of the coordinate plane is in ___.

standard position

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.

tangent

Which trigonometric ratio is calculated by opposite/adjacent

tangent

The ___ side of an angle is the ray of the angle in standard position that does not lie on the x-axis.

terminal

3) The ray of an angle in standard position that does not lie on the x-axis is the ___ of an angle.

terminal side

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

The ratios of the lengths of the two sides of a right triangle are called ___ ratios.

trigonometric

5) The branch of mathematics that deals with the relationships between the sides and the angles of triangles is called ___.

trigonometry

An angle in standard position is an angle with its vertex at the origin and one of its rays on the ___ of the coordinate plane.

x-axis

7) Convert from degrees to radians. 90°= _____ rad

π/2

6) Convert from degrees to radians. 30°= _____ rad

π/6

Convert from degrees to radians. 20°= _____ rad

π9

8) Find the arithmetic mean and geometric mean of the set of numbers.

10 18

15) If `c=10` cm; `x=1.6` cm; find `s_1` .

11.6

Convert from degrees to radians. 55°= _____ rad

11π/36

11) Convert from radians to degrees. 2.5 rad = _____

143.2°

9) Find the arithmetic mean and geometric mean of the set of numbers.

17 32

Convert from radians to degrees. 3 rad = _____

172°

14) If `h=6` in; `y=18` in then find `x.`

2

7) Find the length of side b

2.85 cm

x=1.5 cm; y=5.5 cm; Find h .

2.9

12) Convert from radians to degrees. 4 rad = _____

229.2°

8) Find the length of a

3.7 cm

Use the value s2=6.2 Find sin L.

3/6.2 ≈ 0.5

Use the value s2=6.2 Find cos J.

3/7 0.4

9) Find m∠B to the nearest degree.

47

10) Convert from radians to degrees. 1 rad = _____

57.3°

Convert from degrees to radians. 150°= _____ rad

5π/6

13. c=7: cm; y=5.5cm: Find s2

6.2

Use the value s2=6.2

6.2/3≈2.1

Use the value s2=6.2 Find tan L.

6.2/7 ≈0.4

Use the value s2=6.2 Find tan J.

6.23≈2.1

16) If `c=10` cm; `y=8.4` cm; find `s_2` .

9.17

10) Match the definition with the correct term. Greek mathematician and teacher who lived in the 2nd century B.C.

Hipparchus

1) Which statement is NOT correct?

If you know the lengths of two sides 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.

4) 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

1) Given: `DeltaABC` is a right triangle with altitude `bar(BD)` Prove: `DeltaABC~DeltaCDB~DeltaADB`

SAS Symmetric transitive symmetric AA def. of altitude

7) ___ 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

5) ___ 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

1) ___ ratios are the ratios of the lengths of the two sides of a right triangle.

Trigonometric

_____ is the branch of mathematics that deals with the relationships between the sides and angles of triangles.

Trigonometry

10) Match the trigonometric name with the correct ratio. cos

`"adjacent"/"hypotenuse"`

9) Match the trigonometric name with the correct ratio. sin

`"adjacent"/"hypotenuse"`

11) Match the trigonometric name with the correct ratio. tan

`"opposite"/"adjacent"`

Find cos F.

`3/5`

Find sin D.

`4/3`

Find tan F.

`4/3`

Find cos D.

`4/5`

Find tan D.

`4/5`

Angle of elevation is the angle formed by a horizontal line and a line of sight to a point _____ the horizon.

above

11) Match the definition with the correct term. useful for finding the average of a set of values that are similar

arithmetic mean

The _____ is useful for finding the average of a set of values that are similar.

arithmetic mean

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

d. 30° l. hyp=adj/cosA a. adj=opp/tanA b. 1,200 ft e. adj=600/tan30∘ c. 1,039.9 ft

4) Find the length of c . Use the values sin30∘=0.5,cos30∘=0.866,tan30∘=0.577

e. 30° i. 2.9 cm a. sin A =opp/hyp f. 5.02 cm g. hyp=2.9/sin30∘ j. 5.8 cm

Choose the law and the formula that would be used to solve the triangle.

e. Law of Cosines c. a2=b2+c2-2bccosA

2) Angle of ___ is the angle formed by a horizontal line and line of sight to a point above the horizon.

elevation

5) Choose the law and the formula that would be used to solve the triangle.

f. Law of Cosines d. b2=a2+c2-2accosB

6) Choose the law and the formula that would be used to solve the triangle.

f. Law of Cosines e. c2=a2+b2-2abcosC

4) Choose the law and the formula that would be used to solve the triangle.

f. Law of Sines a. a2=b2+c2-2bccosA

12) Match the definition with the correct term. used to compare values that are proportional

trig mean

8) Convert from degrees to radians. 135°= _____ rad

3π/4

Find sin F.

`3/4`

3) Choose the law and the formula that would be used to solve the triangle.

c. Law of Sines a. sinA/a=sinC/c

2) Choose the law and the formula that would be used to solve the triangle.

g. Law of Sines f. sinA/a=sinC/c

7) The ___ is the positive nth root of the product of n factors.

geometric mean

The _____ is used to compare values that are proportional.

geometric mean

5) Find the length of b . Use the values sin30∘=0.5,cos30∘=0.866,tan30∘=0.577 .

h. 30° a. 2.9 cm b. cosA=adj/hyp f. 5.02 cm g. adj=2.9/tan30∘ i. 5.8 cm

1) Choose the law and the formula that would be used to solve the triangle.

h. Law of Sines e. sinA/a=sinC/c

2) A(n) ___ is a device for measuring the amount of incline or tilt of an object or a surface.

inclinometer

The three expressions, sin-1, cos-1, and tan-1 are called _____ trigonometric functions.

inverse

Find the measure of ∠B

j. 5 cm a. 2.2 cm d. m∠B=cos-1adj/hyp h. m∠B=cos-12.2/5 e. 26°

3) Given the angle of elevation and distance from the Eiffel tower, find its height (x)

k. 40° j. 386 m d. tan=opp/adj f. 324 m c. hyp=386c/os40∘ h. 504 m

6) Find the measure of ∠A

k. 90° i. opp(b) = 3 cm j. m∠A=tan-1 opp/adj d. m∠A=tan-133 h. 5.8 cm

A unit circle is a circle with a radius of ___ unit(s) that has its center at the origin on the coordinate plane.

one

The positive acute angle formed by the terminal side of an angle in standard position and the x-axis is called a ___ angle.

radial

13) If `x=2` cm; `y=8` cm then find the length of the altitude `h.`

4

. Convert from radians to degrees. 0.6 rad = ____

34°