Question

Find the measure of the indicated angle to the nearest degree​

Answer 1

`20^(\circ)`

Explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse.

Let the angle we want to find be
`\theta`.
`\theta`'s adjacent side is 49 and the hypotenuse of the triangle is 52.

Therefore, we have the equation:

`\cos \theta=(49)/(52)`

Take the inverse cosine of both sides:

`\arccos (\cos \theta)=\arccos((49)/(52))`

Simplify using
`\arccos (\cos \theta)=\theta \text{ for }\theta \in (0, 180^(\circ))`:

`\theta=\arccos((49)/(52)),\\\theta=19.557214,\\\theta\approx \boxed{20^(\circ)}`