Answer:
50.8°
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.
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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°.
