Question

Find x. Round your answer to the nearest tenth of a degree.

Answer 1

x = 58.6°

Explanation:

Because this is a right triangle, we're able to find the measure of angle x using one of the trigonometric ratios.

When angle x is the reference angle, the side that is 18 units long is the opposite side and the side that is 11 units long is the adjacent side.

Thus, we can use the tangent ratio, which is given by:

tan (θ) = opposite / adjacent, where

• θ is measure of the reference angle

Thus, we have tan (θ) = 18 / 11

In order to find angle measures we use inverse trigonometry:

tan^-1 (18 / 11) = x

58.57043439 = x

58.6 = x

Thus, the measure of angle x is about 58.6°

Answer 2

`\tan(x )=\cfrac{\stackrel{opposite}{18}}{\underset{adjacent}{11}} \implies \tan^(-1)(~~\tan( x )~~) =\tan^(-1)\left( \cfrac{18}{11} \right) \\\\\\ x =\tan^(-1)\left( \cfrac{18}{11} \right)\implies x \approx 58.6^o`

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