FREE Trigonometry Real-World Applications Questions and Answers

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A surveyor measures the angle of elevation to the top of a building as 45∘. If the surveyor is standing 50 meters away from the building, what is the building’s height?

Correct! Wrong!

At 45∘, the opposite side (height) and adjacent side (distance) are equal in a right triangle. Therefore, the building's height is also 50 meters.

A ship travels 20 km due north, then turns and travels 15 km due east. What is the direct distance between the ship’s starting and ending points?

Correct! Wrong!

The path forms a right triangle, with the distance as the hypotenuse. Using the Pythagorean theorem:
Distance= √20 2+15 2 = √400+225 = √625 = 25 km.

The height of a flagpole casts a shadow 12 meters long when the sun’s elevation angle is 30∘. What is the height of the flagpole?

Correct! Wrong!

Using tan⁡(30∘) = opposite / adjacent:
tan⁡(30∘) = h/12 → √3/3 = h/12 → h= 6 √3

An engineer needs to calculate the height of a tower using trigonometry. From a distance of 100 meters, the angle of elevation to the top of the tower is 60∘. What is the height of the tower?

Correct! Wrong!

Using tan⁡(60∘)=opposite / adjacent:
tan⁡(60∘) = h/100 → √3 =h/100 → h = 100 √3.

A ladder leans against a wall, forming a 60∘ angle with the ground. If the ladder is10 feet long, how high up the wall does it reach?

Correct! Wrong!

The height of the ladder is the opposite side of the triangle.
Using sin⁡(60∘) = opposite / hypotenuse:
sin⁡(60∘) = h/10 → √3/2 = h/10 → h = 5√3.

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