Question

find the sine of ∠f.
h f
80 39
g
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
sin(f) =

Explanation:

Step1: Recall sine definition

For right triangle $\triangle FGH$, $\sin(F) = \frac{\text{opposite side to } \angle F}{\text{hypotenuse}}$

Step2: Identify sides

Opposite side to $\angle F$ is $FG=39$, hypotenuse is $FH$. First solve for $FG$:
$FG = \sqrt{80^2 - 39^2} = \sqrt{6400 - 1521} = \sqrt{4879}$

Step3: Compute sine value

$\sin(F) = \frac{\sqrt{4879}}{80}$

Answer:

$\boldsymbol{\frac{\sqrt{4879}}{80}}$