Question

In $\triangle F H G$, $\angle F H G$ = $90\degree$, F G = 15, G H = 9, H F = 12. Find ratio.

$\tan F$

Solution

VerifiedStep 1

1 of 2Recall that:

$\tan\theta=\dfrac{\text{length of the side {\color{#c34632}\bf{}opposite} to the angle $\theta$}}{\text{length of the side {\color{#c34632}\bf{}adjacent} to the angle $\theta$}}$

Use the given figure to substitute values for the

${\color{#c34632}\bf{}opposite}$

and the

${\color{#c34632}\bf{}adjacent}$

side lengths.

$\tan F=\dfrac{GH}{FH}=\dfrac{9}{12}=\dfrac{3\cdot \cancel{3}}{4\cdot \cancel{3}}=\dfrac{3}{4}$

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