Question

solve this right triangle. give the measures to the nearest tenth.
select one:
a. ∠f = 67°, gh = 18.8 m, fh = 8.7 m
b. ∠f = 77°, gh = 18.8 m, fh = 20.5 m
c. ∠f = 67°, gh = 3.4 m, fh = 8.7 m
d. ∠f = 67°, gh = 18.8 m, fh = 20.5 m

Explanation:

Step1: Find angle $\angle F$

In a right - triangle, the sum of the two non - right angles is $90^{\circ}$. Given one non - right angle $\angle H = 23^{\circ}$, then $\angle F=90^{\circ}-\angle H = 90^{\circ}- 23^{\circ}=67^{\circ}$.

Step2: Find side $GH$

We know that $\tan H=\frac{FG}{GH}$. Given $FG = 80$ m and $\angle H = 23^{\circ}$, then $\tan23^{\circ}=\frac{80}{GH}$. So, $GH=\frac{80}{\tan23^{\circ}}\approx\frac{80}{0.4245}\approx188$ m.

Step3: Find side $FH$

We know that $\sin H=\frac{FG}{FH}$. Given $FG = 80$ m and $\angle H = 23^{\circ}$, then $\sin23^{\circ}=\frac{80}{FH}$. So, $FH=\frac{80}{\sin23^{\circ}}\approx\frac{80}{0.3907}\approx205$ m.

Answer:

D. $\angle F = 67^{\circ}, GH = 188$ m, $FH = 205$ m