Q: A lamp post casts a shadow 25 m long. The angle of elevation of the sun is 51°. What is the height of the lamp post? Which trigonometric ratio should you use to solve for the height?

Use the tangent ratio: $$\tan(51^\circ) = \frac{\text{height}}{25}$$

Q: A hot air balloon is hovering over a point on the ground 95 ft from where you are standing. The angle of elevation to the balloon is 12°. What is the altitude of the balloon?

Altitude $$= 95 \times \tan(12^\circ)$$

Q: You are flying a kite with 90 ft of string stretched straight. The angle of elevation is 35°. Assuming the string forms the hypotenuse, what is the height of the kite above the ground?

Height $$= 90 \times \sin(35^\circ)$$

Q: An airplane climbs at an angle of 16° with the ground and travels 3500 m through the air. What is the horizontal ground distance it covers?

Distance $$= 3500 \times \cos(16^\circ)$$

Q: A lighthouse operator at point P, 45 ft above sea level, sights a sailboat at an angle of depression of 12°. How far is the boat from the base of the lighthouse?

Distance $$= 45 \div \tan(12^\circ)$$

Q: A surveyor measures the angle of elevation to the top of a building as 28°. If she is standing 50 m from the base, what is the height of the building?

Height $$= 50 \times \tan(28^\circ)$$

Q: A pilot sees a runway at an angle of depression of 7°. If the plane is flying at an altitude of 1200 m, how far is the plane from the point on the ground directly below the runway?

Distance $$= 1200 \div \tan(7^\circ)$$

Question 1

A lamp post casts a shadow 25 m long. The angle of elevation of the sun is 51°. What is the height of the lamp post? Which trigonometric ratio should you use to solve for the height?

Accepted Answer

Use the tangent ratio: $$	an(51^\circ) = \frac{	ext{height}}{25}$$

Question 2

A hot air balloon is hovering over a point on the ground 95 ft from where you are standing. The angle of elevation to the balloon is 12°. What is the altitude of the balloon?

Accepted Answer

Altitude $$= 95 	imes 	an(12^\circ)$$

Question 3

You are flying a kite with 90 ft of string stretched straight. The angle of elevation is 35°. Assuming the string forms the hypotenuse, what is the height of the kite above the ground?

Accepted Answer

Height $$= 90 	imes \sin(35^\circ)$$

Question 4

A 25-foot ladder is leaning against a tree. The base of the ladder is 6 feet from the tree. What is the angle $$	heta$$ the ladder makes with the ground?

Accepted Answer

Question 5

A wire reaches from the top of a 130 ft cell tower to the ground, making a 73° angle with the ground. What is the length of the wire?

Accepted Answer

Length $$= 130 \div \sin(73^\circ)$$

Question 6

An airplane climbs at an angle of 16° with the ground and travels 3500 m through the air. What is the horizontal ground distance it covers?

Accepted Answer

Distance $$= 3500 	imes \cos(16^\circ)$$

Question 7

A lighthouse operator at point P, 45 ft above sea level, sights a sailboat at an angle of depression of 12°. How far is the boat from the base of the lighthouse?

Accepted Answer

Distance $$= 45 \div 	an(12^\circ)$$

Question 8

A construction worker needs to place a ladder against a wall so that it reaches a window 20 ft above the ground. If the base of the ladder is 8 ft from the wall, what is the minimum length of the ladder required?

Accepted Answer

Length $$= \sqrt{20^2$ + 8^2$}$$

Question 9

A surveyor measures the angle of elevation to the top of a building as 28°. If she is standing 50 m from the base, what is the height of the building?

Accepted Answer

Height $$= 50 	imes 	an(28^\circ)$$

Question 10

A pilot sees a runway at an angle of depression of 7°. If the plane is flying at an altitude of 1200 m, how far is the plane from the point on the ground directly below the runway?

Accepted Answer

Distance $$= 1200 \div 	an(7^\circ)$$

Question 11

A tree is 18 m tall and casts a shadow of 12 m. What is the angle of elevation of the sun?

Accepted Answer

Angle $$= \arctan\left(\frac{18}{12}\right)$$

Question 12

A cable is attached from the top of a 60 ft pole to the ground at a point 25 ft from the base. What is the angle the cable makes with the ground?

Accepted Answer

Angle $$= \arctan\left(\frac{60}{25}\right)$$

Question 13

A person stands 40 m from a building and measures the angle of elevation to the top as 60°. What is the height of the building?

Accepted Answer

Height $$= 40 	imes 	an(60^\circ)$$

Question 14

A ramp is 15 m long and rises at an angle of 20° with the ground. What is the vertical height gained by the ramp?

Accepted Answer

Height $$= 15 	imes \sin(20^\circ)$$

Question 15

A rescue worker needs to reach a window 30 ft above the ground using a ladder placed 10 ft from the wall. What angle should the ladder make with the ground?

Accepted Answer

Angle $$= \arctan\left(\frac{30}{10}\right)$$

Question 16

A drone is flying at a height of 100 m. If the angle of depression from the drone to a point on the ground is 25°, how far is the point from the drone horizontally?

Accepted Answer

Distance $$= 100 \div 	an(25^\circ)$$

Question 17

A person is standing 30 m from a flagpole and measures the angle of elevation to the top as 45°. What is the height of the flagpole?

Accepted Answer

Height $$= 30 	imes 	an(45^\circ)$$

Question 18

A 50 m cable is attached from the top of a building to the ground at an angle of 60°. What is the height of the building?

Accepted Answer

Height $$= 50 	imes \sin(60^\circ)$$

Question 19

A person is standing 100 m from a tower and measures the angle of elevation to the top as 30°. What is the height of the tower?

Accepted Answer

Height $$= 100 	imes 	an(30^\circ)$$

Question 20

A ramp is 10 m long and rises at an angle of 15° with the ground. What is the vertical height gained by the ramp?

Accepted Answer

Height $$= 10 	imes \sin(15^\circ)$$

Step-by-Step Guidance for Trigonometry Application Problems

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드