Question

In FGH, the measure of H=90°, HF=91 feet, and GH = 50 feet. Find the measure of F to the nearest degree.

Answer 1

Given:

The angle of H=90°, HF=91 feet, and GH = 50 feet.

The objective is to find the measure of angle F.

In the given right angled triangle, the side opposite to the requierd angle is called opposite side, and the other smaller side is called adjacent side.

The trigonometry formula which relates with the opposite and adjacent side is,

$\tan \theta=\frac{opposite}{adjacent}$

Now substitute the value of opposite and adjacent in the above formula to find the value of angle F.

$\begin{gathered} \tan \theta=\frac{50}{91} \\ \theta=\tan ^{-1}(0.549) \\ \theta=28.787^0 \\ \theta\approx29^0 \end{gathered}$

Hence, the value of angle F is 29 degree.