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

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

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Step-by-step 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.


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°.
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