Question

Please help! Help is greatly appreciated. I'm learning the trigonometry unit in my Geometry.

Answer 1

25.1 degrees

Explanation:

So, we’re trying to solve for angle x, and we’ve been given the opposite and the hypotenuse. Recalling SohCahToa, we can figure out that the best trigonometric function for this problem would be sine, as sine is the Opposite/Hypotenuse.

sin(x) = O/H

sin(x) = 4.2/9.9

sin(x) = 0.4242424242…

Next, we need to isolate x. In order to do that, we need the inverse of sin, which is sometimes known as arcsine.

arcsin(sin(x)) = arcsin(0.424242…)

^This part simplifies to just x:

x = arcsin(0.424242…)

Using a calculator, this is found to be 25.1 when rounded to the nearest tenth. Therefore, the answer is x = 25.1 degrees.

Hope this helps!