Question

for the right triangle below, find the measure of the angle.
round your answer to 1 decimal place.
figure is not to scale.
14
6
<--?

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, if the opposite side ($a = 6$) and adjacent side ($b=14$) to the angle $\theta$ are known, we use the tangent ratio. The tangent of an angle in a right - triangle is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan\theta=\frac{6}{14}$.

Step2: Solve for the angle

We know that if $\tan\theta = x$, then $\theta=\tan^{- 1}(x)$. Here, $x = \frac{6}{14}\approx0.4286$. So, $\theta=\tan^{-1}(0.4286)$. Using a calculator, $\tan^{-1}(0.4286)\approx23.2^{\circ}$ (rounded to one decimal place).

Answer:

$23.2^{\circ}$