Question

using trig to find angles
question
solve for x. round to the nearest tenth of a degree, if necessary.
answer
attempt 1 out of 3
x = 。 submit answer

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the tangent of an angle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $x$, the opposite side is $BC = 5$ and the adjacent side is $AB=8.4$. So, $\tan x=\frac{5}{8.4}$.

Step2: Solve for $x$

We know that if $\tan x = a$, then $x=\tan^{- 1}(a)$. So, $x=\tan^{-1}(\frac{5}{8.4})$.
Using a calculator, $\frac{5}{8.4}\approx0.5952$. Then $x=\tan^{-1}(0.5952)$.
Calculating $\tan^{-1}(0.5952)$ on a calculator (in degree mode), we get $x\approx30.8^{\circ}$.

Answer:

$30.8$