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Question

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

tanF\tan F

Solution

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Step 1
1 of 2

Recall that:

tanθ=length of the side opposite to the angle θlength of the side adjacent to the angle θ\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

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

and the

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

side lengths.

tanF=GHFH=912=3343=34\tan F=\dfrac{GH}{FH}=\dfrac{9}{12}=\dfrac{3\cdot \cancel{3}}{4\cdot \cancel{3}}=\dfrac{3}{4}

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