Question

for the right triangle below, find the measure of the angle. figure is not to scale.

Explanation:

Step1: Identify trigonometric - function

We know that for a right - triangle, if we want to find an angle and we know the opposite and adjacent sides to the angle, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Calculate the tangent value

Let the angle we want to find be $\theta$. The opposite side to $\theta$ has length $4$ and the adjacent side has length $6$. So, $\tan\theta=\frac{4}{6}=\frac{2}{3}$.

Step3: Find the angle

To find $\theta$, we take the inverse tangent of $\frac{2}{3}$. $\theta = \arctan(\frac{2}{3})$. Using a calculator in degree mode, $\theta\approx33.7^{\circ}$

Answer:

$\theta\approx33.7^{\circ}$