Question

Find the measure of x.78.3°115ХX== [?]Round your answer to the nearest tenth.

Answer 1

We have the next triangle

And we must find the value of x

In order to find the value of x we must use the given angle

So, we need a trigonometric function that relate the opposite and the adjacent legs of the right triangle

We can see that the trigonometric function we need is tan θ

In this case the angle is 78.3°, the opposite is x and the adjacent is 115

Then, replacing the values in the equation for tan θ

$\tan 78.3^{\circ}=\frac{x}{115}$

Finally, we must solve the equation for x

$\begin{gathered} x=\tan 78.3\cdot115 \\ x=555.3 \end{gathered}$

ANSWER:

$x=555.3$