Q: Which of the following is the correct definition of $$\tan \theta in a $$right triangle?

$$\frac{\text{length of side opposite } \theta}{\text{length of side adjacent to } \theta}$$

Q: Which of the following is a cofunction identity?

$$\sin(90^\circ - \theta) = \cos \theta$$

Question 1

Given a right triangle where the side opposite angle $$	heta is 5 $$units and the hypotenuse is 13 units, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{5}{13}$$

Question 2

Which of the following is the correct definition of $$	an 	heta in a $$right triangle?

Accepted Answer

$$\frac{	ext{length of side opposite } 	heta}{	ext{length of side adjacent to } 	heta}$$

Question 3

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is an $$acute angle in a right triangle, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 4

A ladder leans against a wall, forming a $$60^\circ$$ angle with the ground. If the ladder is 10 feet long, how high up the wall does the ladder reach? (Use $$\sin 60^\circ = \frac{\sqrt{3}}{2})$$

Accepted Answer

$$10 \cdot \frac{\sqrt{3}}{2} = 5\sqrt{3}$$ feet

Question 5

Which trigonometric function is the reciprocal of $$\sin 	heta$$?

Accepted Answer

$$\csc 	heta$$

Question 6

If $$	an 	heta = \frac{a}{b} in a $$right triangle, what is $$\cot 	heta$$?

Accepted Answer

$$\frac{b}{a}$$

Question 7

A surveyor measures the angle of elevation to the top of a building as $$30^\circ$$ from a point 50 meters from the base. How tall is the building? (Use $$	an 30^\circ = \frac{1}{\sqrt{3}})$$

Accepted Answer

$$50 \cdot \frac{1}{\sqrt{3}} \approx 28.87$$ meters

Question 8

What is the value of $$\sin 45^\circ$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 9

Which of the following is a cofunction identity?

Accepted Answer

$$\sin(90^\circ - 	heta) = \cos 	heta$$

Question 10

A pilot sees a runway at an angle of depression of $$5^\circ$$ while flying at an altitude of 2000 meters. How far is the plane from the point on the ground directly below it to the start of the runway? (Use $$	an 5^\circ \approx 0.0875)$$

Accepted Answer

$$\frac{2000}{0.0875} \approx 22,857$$ meters

Question 11

If $$\cos 	heta = \frac{b}{c}$$, which of the following is the correct expression for $$\sec 	heta$$?

Accepted Answer

$$\frac{c}{b}$$

Question 12

Which of the following best describes the angle of elevation?

Accepted Answer

The angle formed by a horizontal line and the line of sight to an object above the horizontal

Question 13

If $$\sin 	heta = \frac{1}{2}$$ and $$	heta is an $$acute angle, what is $$	heta$$?

Accepted Answer

$$30^\circ$$

Question 14

Given a right triangle with sides of length 3, 4, and 5, what is $$	an 	heta if$$ $$	heta is $$the angle opposite the side of length 3?

Accepted Answer

$$\frac{3}{4}$$

Question 15

Which of the following is true for all right triangles regarding trigonometric functions?

Accepted Answer

The value of a trigonometric function depends only on the size of the angle, not the size of the triangle.

Question 16

If $$\csc 	heta = \frac{c}{a}$$, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{a}{c}$$

Question 17

A tree casts a shadow 12 meters long when the angle of elevation of the sun is $$30^\circ. $$How tall is the tree? (Use $$	an 30^\circ = \frac{1}{\sqrt{3}})$$

Accepted Answer

$$12 \cdot \frac{1}{\sqrt{3}} \approx 6.93$$ meters

Question 18

Which of the following is the correct value for $$\cos 60^\circ$$?

Accepted Answer

$$\frac{1}{2}$$

Question 19

If $$\sin 	heta = \cos 	heta$$, what is the value of $$	heta in $$degrees, where $$0^\circ \u003c 	heta \u003c 90^\circ$$?

Accepted Answer

$$45^\circ$$

Right Triangle Trigonometry: Definitions, Special Angles, and Applications

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