We will find the missing measures one at a time. In this case, this means that we want to find m ∠G, FH, and GH.
Angle Measures
To find m∠G, recall that the acute angles of a right triangle are complementary. Therefore, m ∠G and m ∠H add to 90.
m ∠G + m ∠H = 90
Now, we can substitute the given measure of ∠H in our equation and find the measure of ∠G.
m ∠G + 32 = 90 ⇔ m ∠G=58
The sine of ∠H is the ratio of the length of the leg opposite ∠H to the length of the hypotenuse.
sin ∠H=opposite/hypotenuse ⇒ sin 32^(∘) =11/GH
To find the length of GH, we have to use a calculator.
Finally, we can find the measure of FH. To do it, we can use the Pythagorean Theorem.
(GF)^2 + (FH)^2 = (GH)^2
Let's substitute the known lengths, GF = 11 and GH= 20.8, into this equation to find FH.
