Question

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

Answer 1

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°.