Q: Solve for $$x if$$ $$\sin x = 0.2527$$ for $$x in$$ $$[0, 360^\\circ]. $$Round to $$1$$ decimal place.

$$14.6^\\circ$$ and $$165.4^\\circ$$

Q: Solve for $$x if$$ $$\sin x = 0.7138$$ for $$x in$$ $$[0, 360^\\circ]. $$Round to $$1$$ decimal place.

$$45.5^\\circ$$ and $$134.5^\\circ$$

Question 1

A monument has a height of 53.5 feet and the angle of elevation to the top of the monument is $$8.13^\circ. $$How far away from the monument is the observer standing? (Round to the nearest whole foot.)

Accepted Answer

$$377$$ feet

Question 2

A radio tower guy wire attaches to the ground at a $$71^\circ$$ angle and the wire is $$1,322$$ feet long. How tall is the radio tower to the nearest whole foot?

Accepted Answer

$$1,251$$ feet

Question 3

A ramp is $$4$$ feet long and must rise $$1$$ inch per foot of length. What is the angle of elevation to the nearest tenth of a degree?

Accepted Answer

$$1.2^\circ$$

Question 4

Solve for $$x if$$ $$\sin x = 0.2527$$ for $$x in$$ $$[0, 360^\circ]. $$Round to $$1$$ decimal place.

Accepted Answer

$$14.6^\circ$$ and $$165.4^\circ$$

Question 5

Solve for $$x if$$ $$\sin x = 0.7138$$ for $$x in$$ $$[0, 360^\circ]. $$Round to $$1$$ decimal place.

Accepted Answer

$$45.5^\circ$$ and $$134.5^\circ$$

Question 6

A surveyor stands $$200$$ feet from the base of a building and measures the angle of elevation to the top as $$30^\circ. $$What is the height of the building?

Accepted Answer

$$115.5$$ feet

Question 7

A ladder $$20$$ feet long leans against a wall, making a $$65^\circ$$ angle with the ground. How high up the wall does the ladder reach?

Accepted Answer

$$18.1$$ feet

Question 8

A pilot spots a runway at an angle of depression of $$12^\circ$$ from a height of $$1,500$$ feet. How far is the plane from the runway horizontally?

Accepted Answer

$$7,180$$ feet

Question 9

A tree casts a shadow $$25$$ feet long when the angle of elevation of the sun is $$40^\circ. $$What is the height of the tree?

Accepted Answer

$$20.1$$ feet

Question 10

A ship is $$500$$ meters from a lighthouse. The angle of elevation to the top of the lighthouse is $$5^\circ. $$What is the height of the lighthouse?

Accepted Answer

$$43.7$$ meters

Question 11

A ramp for wheelchair access rises $$2$$ feet over a horizontal distance of $$24$$ feet. What is the angle of elevation of the ramp?

Accepted Answer

$$4.8^\circ$$

Question 12

A firefighter needs to reach a window $$30$$ feet above the ground. If the ladder must be placed $$10$$ feet from the building, what angle should the ladder make with the ground?

Accepted Answer

$$71.6^\circ$$

Question 13

A cable is attached from the top of a $$60$$ foot pole to the ground $$25$$ feet away. What is the angle the cable makes with the ground?

Accepted Answer

$$67.4^\circ$$

Question 14

A person standing $$100$$ feet from a building sees the top at an angle of elevation of $$20^\circ. $$How tall is the building?

Accepted Answer

$$36.4$$ feet

Question 15

A $$15$$ foot ladder is placed so that it reaches a window $$12$$ feet above the ground. What is the angle the ladder makes with the ground?

Accepted Answer

$$53.1^\circ$$

Question 16

A ramp is $$10$$ feet long and rises $$2$$ feet. What is the angle of elevation of the ramp?

Accepted Answer

$$11.5^\circ$$

Question 17

A $$25$$ foot flagpole casts a shadow $$18$$ feet long. What is the angle of elevation of the sun?

Accepted Answer

$$54.5^\circ$$

Question 18

A $$40$$ foot ladder leans against a building, making a $$70^\circ$$ angle with the ground. How high up the building does the ladder reach?

Accepted Answer

$$37.6$$ feet

Question 19

A $$50$$ foot wire is attached from the top of a pole to the ground $$30$$ feet away. What is the angle the wire makes with the ground?

Accepted Answer

$$53.1^\circ$$

Question 20

A $$100$$ foot building casts a shadow $$60$$ feet long. What is the angle of elevation of the sun?

Accepted Answer

$$59^\circ$$

Applications of Trigonometric Functions in Right Triangles

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드