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 F

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

Step2: Find side GH

We know that $\tan H=\frac{FG}{GH}$. Given $FG = 8.0$ m and $\angle H = 23^{\circ}$, then $GH=\frac{FG}{\tan H}$.
$GH=\frac{8.0}{\tan23^{\circ}}\approx\frac{8.0}{0.4245}\approx18.8$ m

Step3: Find side FH

We know that $\sin H=\frac{FG}{FH}$. Given $FG = 8.0$ m and $\angle H = 23^{\circ}$, then $FH=\frac{FG}{\sin H}$.
$FH=\frac{8.0}{\sin23^{\circ}}\approx\frac{8.0}{0.3907}\approx20.5$ m

Answer:

d. $\angle F = 67^{\circ}, GH = 18.8$ m, $FH = 20.5$ m