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luisejr77

Answer: m∠F=67°

Step-by-step explanation:

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

[tex]FG=5\\HG=12\\FH=13[/tex]

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

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

Where the opposite side is 12, the adjacent side is 5 and the angle [tex]\alpha[/tex] is m∠F.

Then, substituting values into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]:

[tex]F=arctan(\frac{12}{5})\\F=67.38\°[/tex]

To the nearest degree:

m∠F=67°

lublana

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.

[tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}=\frac{GH}{GF}[/tex]

[tex]\tan\left(F\right)=\frac{12}{5}[/tex]

[tex]F=\tan^{-1}\left(\frac{12}{5}\right)[/tex]

[tex]F=67.38[/tex] degree

Which is approx m∠F=67°

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