Chapter 14 Geometry
You are standing at the point (2,3) on a graph. Which point is closer: (-1,2) or (4,6)?
(-1,2) - Finding Distance with the Pythagorean Theorem
Simplify the following expression. sin20/(1+cos0)(1-cos0) - tan2 0/(sec0-1)(sec0+1)
0 - List of the Basic Trig Identities
What is the formula to find the area of a triangle with a known height?
1/2 base times height - Using Sine to Find the Area of a Triangle
In the pictured triangle, ∠A is 137 degrees and ∠B is 28 degrees. If side b is 71 units long, approximately how long is side a?
103 units - Law of Sines: Definition and Application
What is the area of the diamond/kite shown below?
12 units2 - How to Calculate the Volumes of Basic Shapes
In the pictured triangle, side a is 9 and side b is 6. If ∠C is 26 degrees, then approximately how long is side c? Round the value of the cosine to 2 decimal places.
4
Jerry wants to buy a TV online, but the ad for the TV he wants does not say what the screen size is. He knows that TV screens are measured diagonally. The ad states the height and width of the screen, so he uses the Pythagorean Theorem to determine what the screen size is. What is the screen size of the TV that Jerry wants to buy?
40 inches - Finding Distance with the Pythagorean Theorem
Find the value of x, rounded to the nearest degree.
75 degrees - Practice Finding the Trigonometric Ratios
What is x?
NOT 1.5 - Trigonometry and the Pythagorean Theorem
Sin θ is defined as:
opposite / hypotenuse - Trigonometry: Sine and Cosine
What is z in terms of x?
sqrt(x^2-1)- Trigonometry and the Pythagorean Theorem
What's the value of 2sin(θ)cos(θ) given that the equation below is true? sin0+cos0^2=1
0- List of the Basic Trig Identities
What is x?
0.6 x=cos0 - Trigonometry: Sine and Cosine
What is x?
0.8 x=sin0 - Trigonometry: Sine and Cosine
Simplify the following expression. (secO+tanO) (secO-tanO)
1 - List of the Basic Trig Identities
What is the value of cos(θ) given that the equation below is true? cot 0(cot 0 + sin 0) =csc2 0
1 - List of the Basic Trig Identities
What is x? x=sin^2 0 +cos^2 0
1 - Trigonometry and the Pythagorean Theorem
What is the area of the circle enclosed by taking a 4 cm by 6 cm sheet and wrapping it around a 6 cm tall cylinder?
1.27 square cm - How to Solve Visualizing Geometry Problems
What is x?
1.33 x=tan0 - Trigonometry: Sine and Cosine
What is the formula for finding the area of a triangle with an unknown height?
1/2 a times b times sine C - Using Sine to Find the Area of a Triangle
What is the volume of an open-ended cube that has a surface area of 125 square meters?
125 cubic meters - How to Solve Visualizing Geometry Problems
In the pictured triangle, ∠A is 62 degrees and ∠C is 86 degrees. If side a is 112 units long, approximately how long is side c?
127 units - Law of Sines: Definition and Application
What is the area of the annulus/doughnut shown below?
12pi - How to Calculate the Volumes of Basic Shapes
Find the distance between a and b.
13 - Finding Distance with the Pythagorean Theorem
Find the value of x, rounded to the nearest tenth.
15.7 - Practice Finding the Trigonometric Ratios
In the pictured triangle, ∠A is 98 degrees and ∠B is 12 degrees. If side a is 84 units long, approximately how long is side b?
18 units - Law of Sines: Definition and Application
What is the volume of a hemisphere with a radius of 3cm?
18π cm3 - How to Calculate the Volumes of Basic Shapes
In the pictured triangle, side b is 12 and side c is 16. If ∠A is 84 degrees, then approximately how long is side a? Round the value of the cosine to 2 decimal places.
19
Find the value of x, rounded to the nearest tenth.
19.1 - Practice Finding the Trigonometric Ratios
What is the volume of a cube with an edge length of 6 cm?
216 cm3 - How to Calculate the Volumes of Basic Shapes
In the pictured triangle, ∠A is 81 degrees and ∠B is 67 degrees. If side a is 34 units long, approximately how long is side b?
32 units - Law of Sines: Definition and Application
Find the value of x, rounded to the nearest degree.
35 degrees - Practice Finding the Trigonometric Ratios
In the pictured triangle, side a is 17 and side c is 20. If ∠B is 19 degrees, then approximately how long is side b? Round the value of the cosine to 2 decimal places.
7
What is the area of the circle enclosed by taking a 10 cm by 6 cm sheet and wrapping it so that the short edges touch?
7.96 square cm - How to Solve Visualizing Geometry Problems
What is the volume of the cube created by taking two 6 by 2 strips of paper, folding them into thirds, and using each third as a side of the square?
8 cubic inches - How to Solve Visualizing Geometry Problems
In the pictured triangle, side a is 32, side b is 24, and side c is 37. What is the approximate measure of ∠C? When calculating the inverse cosine, round the initial value to 2 decimal places.
81 degrees
In the pictured triangle, ∠A is 58 degrees and ∠C is 63 degrees. If side a is 84 units long, approximately how long is side c?
88 units - Law of Sines: Definition and Application
What is the area of the right triangle shown below?
96 feet squared - How to Calculate the Volumes of Basic Shapes
What is the trigonometric ratio for cosine?
Adjacent/Hypotenuse - Trigonometric Ratios and Similarity
In calculating the area of a triangle, why do you multiply by 1/2?
Because a triangle is essentially a split rectangle - Using Sine to Find the Area of a Triangle
Find the value of x, rounded to the nearest tenth.
NOT 21.4 - Practice Finding the Trigonometric Ratios
In the pictured triangle, side a is 23, side b is 18, and side c is 16. What is the approximate measure of ∠C? When calculating the inverse cosine, round the initial value to 2 decimal places.
NOT 41 degrees
What part of the usual formula does 'b times sine C' replace?
NOT This part of the formula does not replace any part of the triangle; it's completely new. - Using Sine to Find the Area of a Triangle
In the pictured triangle, what ratio represents the cosine of theta?
NOT XY/ZY - Trigonometric Ratios and Similarity
What is the trigonometric ratio for tangent?
Opposite/Adjacent - Trigonometric Ratios and Similarity
What is the trigonometric ratio for sine?
Opposite/Hypotenuse - Trigonometric Ratios and Similarity
Which of the following is true?
Point b is ~0.45 units further away from c than a is. - Finding Distance with the Pythagorean Theorem
In using sine to find the area of a triangle, what kind of imaginary triangle is being created?
Right - Using Sine to Find the Area of a Triangle
What is the acronym to remember sine, cosine and tangent?
SOH CAH TOA - Trigonometric Ratios and Similarity
The Pythagorean Theorem states that a^2 + b^2 = c^2. What are a, b, and c?
The sides and hypotenuse of a right triangle. - Trigonometry and the Pythagorean Theorem
What is x?
The tangent is always equal to the opposite over adjacent, so this tangent is referring to the phi angle. - Trigonometry: Sine and Cosine
If we want to find the surface area of the inside of a swimming pool with the dimensions 2 m deep x 10 m wide x 30 m long, then why is this surface area different from a rectangular prism with the dimensions 2 m deep x 10 m wide x 30 m long?
Unlike the prism, the pool has no top surface. - How to Solve Visualizing Geometry Problems
What is the Pythagorean Theorem and how is it used?
a2 + b2 = c2 ; it is used to find the length of a side of a right triangle when given the lengths for the other two sides - Finding Distance with the Pythagorean Theorem
What's the value of sec2 (θ) given that the equation below is true? sin2Otan2O+sin2O=pi
pi/sin2O - List of the Basic Trig Identities
What is z in terms of x and y?
z=x/sgrt(x^2+y^2) - Trigonometry and the Pythagorean Theorem