Question

current attempt in progress
refer to the following right triangle:
given ( a = 81 mathrm{~mm} ) and ( c = 97 mathrm{~mm} ), find ( \beta ). round your answer to the nearest degree.
( \beta = ) i ( circ )

Explanation:

Step1: Recall the cosine function

In a right - triangle, \(\cos\beta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(\beta\) is \(a = 81\) mm and the hypotenuse \(c = 97\) mm. So, \(\cos\beta=\frac{a}{c}\).
Substitute \(a = 81\) and \(c = 97\) into the formula: \(\cos\beta=\frac{81}{97}\approx0.835\).

Step2: Find the angle using the inverse cosine function

We know that \(\beta=\cos^{- 1}(\cos\beta)\). Since \(\cos\beta\approx0.835\), then \(\beta=\cos^{-1}(0.835)\).
Using a calculator, \(\cos^{-1}(0.835)\approx33.4^{\circ}\).

Answer:

\(33\)