Question

for the right triangle below, find the measure of the angle. round your answer to 1 decimal place. figure is not to scale.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\), and \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the side opposite to the unknown angle is \(9\) and the hypotenuse is \(14\). So, we use the sine inverse function. Let the unknown angle be \(\theta\). Then \(\sin\theta=\frac{9}{14}\).

Step2: Calculate the angle

We know that \(\theta=\sin^{- 1}(\frac{9}{14})\). Using a calculator, \(\sin^{-1}(x)\) where \(x = \frac{9}{14}\approx0.6429\). \(\sin^{-1}(0.6429)\approx40.0^{\circ}\) (rounded to 1 decimal place).

Answer:

\(40.0^{\circ}\)