Find the measure of the indicated angle to the nearest degree

39

Explanation:

In this case, we must first find the hypotenuse of this triangle by the Pythagorean Theorem.

sqrt(a^2 + b^2) = c

1) sqrt( 23^2 + 28^2) = c
2) sqrt(529 + 784) = c
3) sqrt(1313) = c
4) c = 36.2353

Now that we have obtained our hypotenuse, we can easily find our missing angle by the sine rule.

sin(Angle)/opposing side = sin(Angle)/opposing side

1) sin90/36.2353 = sinx/23
2) 1/36.2353 = sinx/23
3) 23/36.2353 = sinx
4) x = sin^-1(23/36.2353) (SHIFT + Sin on your calculator to do this)
5) x ≈ 39

Hope this helps, brainliest would be appreciated :)