Q: A surveyor stands 50 meters from the base of a building and measures the angle of elevation to the top as $$30^ ext{o}. $$What is the height of the building above the surveyor's eye level? (Assume the ground is level.)

$$50 \times \tan(30^ ext{o}) = 28.87$$ meters

Q: A ladder leans against a wall, making a $$60^ ext{o}$$ angle with the ground. If the foot of the ladder is 4 meters from the wall, how high does the ladder reach up the wall?

$$4 \times \tan(60^ ext{o}) = 6.93$$ meters

Q: A pilot sees a runway at an angle of depression of $$5^ ext{o}$$ from an altitude of 1200 meters. How far is the runway horizontally from the plane?

$$1200 \div \tan(5^ ext{o}) = 13,722$$ meters

Q: A construction worker needs to reach a window 10 meters above the ground. If the ladder must be placed 6 meters from the wall, what angle should the ladder make with the ground?

$$\tan$$^{-1}$$(10/6) = 59^ ext{o}$$

Q: A rescue worker spots a stranded hiker at an angle of elevation of $$15^ ext{o}$$ from a point 200 meters horizontally away. How high above the rescue worker is the hiker?

$$200 \times \tan(15^ ext{o}) = 53.6$$ meters

Q: A person observes the top of a tower at an angle of elevation of $$45^ ext{o}$$ while standing 100 meters from its base. What is the height of the tower?

$$100 \times \tan(45^ ext{o}) = 100$$ meters

Question 1

Which of the following best describes the process of 'solving a right triangle'?

Accepted Answer

Determining the measures of all angles and the lengths of all sides, given certain information.

Question 2

A surveyor stands 50 meters from the base of a building and measures the angle of elevation to the top as $$30^	ext{o}. $$What is the height of the building above the surveyor's eye level? (Assume the ground is level.)

Accepted Answer

$$50 	imes 	an(30^	ext{o}) = 28.87$$ meters

Question 3

If you know the measures of two sides of a right triangle, which of the following is always possible?

Accepted Answer

You can determine the measure of the third side and all angles.

Question 4

An observer in a hot air balloon sees an airplane flying below. The angle between the horizontal and the line of sight to the airplane is called:

Accepted Answer

Angle of depression

Question 5

A ladder leans against a wall, making a $$60^	ext{o}$$ angle with the ground. If the foot of the ladder is 4 meters from the wall, how high does the ladder reach up the wall?

Accepted Answer

$$4 	imes 	an(60^	ext{o}) = 6.93$$ meters

Question 6

Which statement is true about right triangles with the same three angle measures?

Accepted Answer

They may have different side lengths but are always similar.

Question 7

A pilot sees a runway at an angle of depression of $$5^	ext{o}$$ from an altitude of 1200 meters. How far is the runway horizontally from the plane?

Accepted Answer

$$1200 \div 	an(5^	ext{o}) = 13,722$$ meters

Question 8

If you are given only the measures of the two non-right angles in a right triangle, what can you determine?

Accepted Answer

You can determine the ratios of the sides but not their actual lengths.

Question 9

A construction worker needs to reach a window 10 meters above the ground. If the ladder must be placed 6 meters from the wall, what angle should the ladder make with the ground?

Accepted Answer

$$	an$$^{-1}$$(10/6) = 59^	ext{o}$$

Question 10

Which trigonometric function relates the angle of elevation to the ratio of the opposite side over the adjacent side in a right triangle?

Accepted Answer

$$	an(	heta)$$

Question 11

A rescue worker spots a stranded hiker at an angle of elevation of $$15^	ext{o}$$ from a point 200 meters horizontally away. How high above the rescue worker is the hiker?

Accepted Answer

$$200 	imes 	an(15^	ext{o}) = 53.6$$ meters

Question 12

Which of the following is NOT sufficient information to solve a right triangle completely?

Accepted Answer

All three angle measures

Question 13

A person observes the top of a tower at an angle of elevation of $$45^	ext{o}$$ while standing 100 meters from its base. What is the height of the tower?

Accepted Answer

$$100 	imes 	an(45^	ext{o}) = 100$$ meters

Question 14

Which real-world scenario best illustrates the use of the angle of depression?

Accepted Answer

A lifeguard looking down at a swimmer from a tower.

Question 15

A drone is flying at a constant altitude of 80 meters. If the angle of depression from the drone to a landing pad is $$20^	ext{o}$$, how far is the landing pad horizontally from the drone?

Accepted Answer

$$80 \div 	an(20^	ext{o}) = 219.8$$ meters

Question 16

If the angle of elevation to the top of a building is $$60^	ext{o}$$ from a point 30 meters away, what is the height of the building?

Accepted Answer

$$30 	imes 	an(60^	ext{o}) = 51.96$$ meters

Question 17

A firefighter needs to reach a window 8 meters above the ground. If the ladder is placed 5 meters from the wall, what is the length of the ladder required?

Accepted Answer

$$\sqrt{8^2$ + 5^2$} = 9.43$$ meters

Question 18

Which of the following is the correct definition of the angle of elevation?

Accepted Answer

The angle between the horizontal and the line of sight to an object above the horizontal.

Right Triangle Applications in Trigonometry

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