Question

What is the answer to this question?

Answer 1

m∠F=67°

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)=(opposite)/(adjacent)=(GH)/(GF)`

`\tan\left(F\right)=(12)/(5)`

`F=\tan^(-1)\left((12)/(5)\right)`

`F=67.38` degree

Which is approx m∠F=67°

Answer 2

Answer: m∠F=67°

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((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((opposite)/(adjacent))`:

`F=arctan((12)/(5))\\F=67.38\°`

To the nearest degree:

m∠F=67°