Question

for the right triangle below, find the measure of the angle. please show your answer to one decimal place.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Let the unknown angle be \(\theta\). The side opposite to \(\theta\) is \(10\), and the hypotenuse is \(12\). So, \(\sin\theta=\frac{10}{12}\).

Step2: Calculate the angle

We know that \(\theta = \sin^{- 1}(\frac{10}{12})\). First, simplify \(\frac{10}{12}=\frac{5}{6}\approx0.833\). Then, \(\theta=\sin^{-1}(0.833)\). Using a calculator, \(\sin^{-1}(0.833)\approx56.4^{\circ}\)

Answer:

\(56.4^{\circ}\)