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Name: ___________ Geometry - Trigonometry Review Problems Question 1 Find the value of x, y, and angle B. The angle in the bottom right corner is a right angle. Question 2 a) The sin(ϴ) is 10/13. The cos(ϴ) is 12/13. What is the tan(ϴ)? b) The sin(ϴ) is 5/14. The tan(ϴ) is 5/10. What is the cos(ϴ)? Question 3 a) cos(ϴ) = 2/3. Find the value of sin(ϴ) b) tan(ϴ) = 3. Find the value of cos(ϴ) c) 1/sin(ϴ) = 7/4. Find the value of tan(ϴ)

Name: Geometry - Trigonometry Review - … · Name: _____ Geometry - Trigonometry Review Problems Question 1 Find the value of x, y, and angle B. The angle in the bottom right corner

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Page 1: Name: Geometry - Trigonometry Review - … · Name: _____ Geometry - Trigonometry Review Problems Question 1 Find the value of x, y, and angle B. The angle in the bottom right corner

Name: ___________

Geometry - Trigonometry Review

Problems

Question 1

Find the value of x, y, and angle B. The angle in the bottom right corner is a right angle.

Question 2

a) The sin(ϴ) is 10/13. The cos(ϴ) is 12/13. What is the tan(ϴ)?

b) The sin(ϴ) is 5/14. The tan(ϴ) is 5/10. What is the cos(ϴ)?

Question 3

a) cos(ϴ) = 2/3. Find the value of sin(ϴ)

b) tan(ϴ) = 3. Find the value of cos(ϴ)

c) 1/sin(ϴ) = 7/4. Find the value of tan(ϴ)

Page 2: Name: Geometry - Trigonometry Review - … · Name: _____ Geometry - Trigonometry Review Problems Question 1 Find the value of x, y, and angle B. The angle in the bottom right corner

Question 4

A nursery plants a new tree and attaches a wire to help support the tree while its roots take hold. An eight

foot wire is attached to the tree and to a stake in the ground. From the stake in the ground the angle of

elevation of the connection with the tree is 42º. Find to the nearest tenth of a foot, the height of the

connection point on the tree.

Question 5

From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º.

If the tower is 45 feet in height, how far is the partner from the base of the tower, to the nearest tenth of a

foot?

Question 6

A kite held by 125m of string makes an angle of elevation with the ground of 45º. About how high is the kite

above the ground?

Question 7

a) Solve for m<R b) Solve for x.

Page 3: Name: Geometry - Trigonometry Review - … · Name: _____ Geometry - Trigonometry Review Problems Question 1 Find the value of x, y, and angle B. The angle in the bottom right corner

Question 8

Based on the triangle below, write the full equation for every trig ratio (sin, cos, and tan) for every angle you

can.

Question 9

a) Solve for b. b) Solve for m<A.

Question 10

a) Find the value of ϴ that makes the following true: sin(ϴ + 10) = cos(ϴ - 20)

Page 4: Name: Geometry - Trigonometry Review - … · Name: _____ Geometry - Trigonometry Review Problems Question 1 Find the value of x, y, and angle B. The angle in the bottom right corner

b) Find the value of ϴ that makes the following true: sin(ϴ + x) = cos(ϴ - x)

c) Find every value between 0o and 90o that makes the following false: sin(ϴ) = cos(ϴ)

Question 11

If sin(ϴ) = 4/7, use the Pythagorean Identity to find the cos(ϴ).

Question 12

Find the area of the two triangles in question 9.

Question 13

If arcsin(𝑥

𝑦) = arccos(z), find an expression for z in terms of x and y.

Question 14

Explain why the following equations are impossible:

a) sin(ϴ) = 9/8

b) tan(45o) = 𝑥+1

𝑥

c) sin(90o) = cos(90o)

d) arctan(𝑥

𝑦) = arcsin(

𝑥

𝑥−𝑦)

Question 15

Use a trig identity to express the following only in terms of sin(ϴ) or cos(ϴ):

a) tan(ϴ)

b) 1/tan(ϴ)

c) sin(ϴ)tan(ϴ)

d) tan(ϴ)/sin(ϴ)