Question

Please help me solve

Answer 1

D

Explanation:

First, to find the length of the side FH we will use the Pythagorean theorem which states
`a^2+b^2=c^2`. We can say that FH = a, FG = b, and HG = c. Since we know the values of b and c, we will rearrange the formula to solve for a
`a = √(c^2-b^2)`. That will be
`\sqrt{18^2-12^2)` which gives us 13.4 for the missing side.

Now to solve for the angles we will use simple trigonometry. Since we know that
`sin(\theta) = \frac{opposite} {hypotenuse}`, we can do inverse trigonometry for the missing angles
`sin^(-1)((opposite)/(adjacent)) = \theta`. For angle H, we can do
`sin^(-1)((12)/(18))` which gives us 41.8 degrees. For angle G we can do
`sin^(-1)((13.4)/(18))` and we get 48.1 degrees. We could also use inverse cos and trig to solve it.

Looking at the answer choices, only answer choice D is correct.