Question 1

Given a right triangle with legs of length $$3$$ and $$4$$, what is the length of the hypotenuse?

Accepted Answer

$$5$$

Question 2

If $$	an 	heta = -1.281$$, what is the value of $$	heta in $$degrees, rounded to the nearest integer, where $$0^\circ \u003c 	heta \u003c 360^\circ$$?

Accepted Answer

$$307^\circ$$

Question 3

A ramp rises $$5$$ meters over a horizontal distance of $$25$$ meters. What is the angle of elevation of the ramp, to the nearest degree?

Accepted Answer

$$11^\circ$$

Question 4

If $$\cot 	heta = 0.540$$, what is $$	heta in $$degrees, where $$0^\circ \u003c 	heta \u003c 360^\circ$$?

Accepted Answer

$$61.54^\circ$$

Question 5

Given $$	an \beta = -1.281$$, which of the following is a possible value for $$\beta in $$degrees?

Accepted Answer

$$307^\circ$$

Question 6

If $$	heta = 360^\circ - 52.023^\circ$$, what is the value of $$	heta$$?

Accepted Answer

$$307.977^\circ$$

Question 7

A ladder leans against a wall, making an angle $$	heta$$ with the ground. If the top of the ladder is $$8$$ meters above the ground and the base is $$6$$ meters from the wall, what is the length of the ladder?

Accepted Answer

$$10$$ meters

Question 8

If $$	an 	heta = 0.781$$, what is $$	heta in $$degrees, rounded to the nearest integer?

Accepted Answer

$$38^\circ$$

Question 9

Which of the following is the correct value for $$	an$$^{-1}$$(-1.281) in $$degrees, rounded to two decimal places?

Accepted Answer

$$-52.02^\circ$$

Question 10

A surveyor measures the angle of elevation to the top of a building as $$38^\circ$$ from a point $$50$$ meters from the base. What is the height of the building to the nearest meter?

Accepted Answer

$$39$$ meters

Question 11

If $$	an 	heta = 1$$, what is the value of $$	heta in $$degrees between $$0^\circ$$ and $$360^\circ$$?

Accepted Answer

$$45^\circ$$ and $$225^\circ$$

Question 12

A ship sails $$8 km $$east and then $$6 km $$north. How far is the ship from its starting point?

Accepted Answer

$$10 km$$

Question 13

If $$	an 	heta = 0.540$$, what is the value of $$	heta in $$degrees, rounded to two decimal places?

Accepted Answer

$$28.46^\circ$$

Question 14

A right triangle has an angle $$	heta$$ such that $$\sin 	heta = 0.6. $$What is $$	heta in $$degrees, rounded to the nearest integer?

Accepted Answer

$$37^\circ$$

Question 15

If $$	an 	heta = -1.281$$ and $$0^\circ \u003c 	heta \u003c 360^\circ$$, which quadrant does $$	heta$$ lie in?

Accepted Answer

Quadrant IV

Question 16

A 25-foot ladder leans against a wall, reaching a height of 20 feet. What is the angle the ladder makes with the ground, to the nearest degree?

Accepted Answer

$$53^\circ$$

Question 17

If $$	an 	heta = 0.781$$, what is $$	heta in $$radians, rounded to two decimal places?

Accepted Answer

$$0.67$$ radians

Question 18

A building casts a $$12$$ meter shadow when the angle of elevation of the sun is $$52^\circ. $$What is the height of the building to the nearest meter?

Accepted Answer

$$15$$ meters

Question 19

If $$	an 	heta = -1.281$$ and $$	heta is $$between $$180^\circ$$ and $$360^\circ$$, what is the reference angle for $$	heta$$?

Accepted Answer

$$52.02^\circ$$

Question 20

A road rises $$8$$ meters vertically for every $$15$$ meters horizontally. What is the angle of inclination of the road, to the nearest degree?

Accepted Answer

$$28^\circ$$

Angles, Trigonometric Functions, and Their Applications in Precalculus

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