Question

What is the answer to this question?

Answer 1

Answer:

m∠F=67°

Step-by-step explanation:

We have been given triangle FGH which is right angle at G.

Sides has length:

GH = 12

GF = 5

FH = 13

Using those values we need to find the measure of angle F to the nearest degree.

So we can use trigonometric ratios to get that.

$\tan\left(\theta\right)=\frac{opposite}{adjacent}=\frac{GH}{GF}$

$\tan\left(F\right)=\frac{12}{5}$

$F=\tan^{-1}\left(\frac{12}{5}\right)$

$F=67.38$ degree

Which is approx m∠F=67°

Answer 2

Answer: m∠F=67°

Step-by-step explanation:

Given the right triangle FHG and the lengths of all its sides:

$FG=5\\HG=12\\FH=13$

You can calculate the measure of the angle identified as m∠F with:

$\alpha=arctan(\frac{opposite}{adjacent})$

Where the opposite side is 12, the adjacent side is 5 and the angle $\alpha$ is m∠F.

Then, substituting values into $\alpha=arctan(\frac{opposite}{adjacent})$:

$F=arctan(\frac{12}{5})\\F=67.38\°$

To the nearest degree:

m∠F=67°