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Other word problems relating angles in trigonometry

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Angle Word Problems in Trigonometry

Trigonometry angle word problems describe a real object, such as a kite string, that forms a right triangle with the ground. Learn to identify the hypotenuse, angle, and known side, then solve for height or distance using sine and cosine, with a worked example.

Setting up an angle word problem

Many trigonometry word problems describe a real object — a kite string, a shadow, a ramp — that forms a right triangle with the ground. The key step is always the same: identify the hypotenuse (the diagonal, often a string, rope, or line of sight), the angle given, and which side you're solving for.

Angle word problem: kite string A kite string 40 meters long makes a 52 degree angle with the ground. Using sine, the kite's height is about 31.5 meters. Using cosine, the horizontal distance from the flier is about 24.6 meters. 52° height ≈ 31.5 m horizontal ≈ 24.6 m string = 40 m
A 40-meter kite string at 52° puts the kite about 31.5 m up and 24.6 m out horizontally.

A kite string is 40 meters long and makes a 52° angle with the ground. How high is the kite, and how far out horizontally is it?

Height (SOH): sin 52° = height / 40, so height = 40 · sin 52° ≈ 31.5 m.

Horizontal distance (CAH): cos 52° = horizontal / 40, so horizontal = 40 · cos 52° ≈ 24.6 m.

This is the same triangle setup as a ladder problem or a guy wire problem — only the object and the labels change. Once the triangle is drawn with its angle and known side marked, choosing sine, cosine, or tangent from SOHCAHTOA is the same process every time.

Draw the triangle first, even a rough sketch. Label the angle, mark the side you know, and mark the side you need. This turns a wordy problem into the same short calculation every time.

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