Question

The hypotenuse of a right triangle measures 2 square root 15 centimeters and its shorter leg measures 2 square root 6

centimeters.

What is the measure of the larger acute angle of the triangle? Round your answer to the nearest
tenth of a degree.

Answer 1

50.8°

Explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between side lengths and trig functions for a right triangle. Here, you are given the short side and the hypotenuse, and asked for the largest acute angle.

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The short side is adjacent to the largest acute angle, so the relevant relation is ...

Cos = Adjacent/Hypotenuse

cos(β) = (2√6)/(2√15) = √0.4

The angle measure is found using the inverse cosine function:

β = arccos(√0.4) ≈ 50.8°

The larger acute angle is about 50.8°.