Question

for the right triangle below, find the measure of the angle. figure is not to scale. 8 6 <--? a° degrees

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to angle $A$ is $8$ and the adjacent side is $6$. So, $\tan(A)=\frac{8}{6}=\frac{4}{3}$.

Step2: Find the angle

We know that if $\tan(A) = x$, then $A=\arctan(x)$. So, $A = \arctan(\frac{4}{3})$. Using a calculator in degree mode, $A\approx53.13^{\circ}$.

Answer:

$53.13$