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# Help!

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In right triangle XYZ with $$\angle YXZ = 90^\circ$$, we have XY = 24 and YZ = 25. Find $$\tan Y$$.

Mar 7, 2019

#1
+23526
+1

In right triangle $$XYZ$$ with $$\angle YXZ = 90^\circ$$, we have $$XY = 24$$ and $$YZ = 25$$. Find $$\tan Y$$.

$$\begin{array}{|rcll|} \hline 24^2+XZ^2 &=& 25^2 \\ XZ^2 &=& 25^2-24^2 \\ &=& (24+1)^2 - 24^2 \\ &=& 24^2 + 48 + 1 - 24^2 \\ &=& 49 \\ &=& 7^2 \\ \mathbf{XZ} &\mathbf{=} & \mathbf{7} \\\\ \tan(Y) &=& \dfrac{XZ}{24} \\ \mathbf{\tan(Y)} &\mathbf{=} & \mathbf{\dfrac{7}{24}} \\ \hline \end{array}$$

Mar 7, 2019
#2
+7761
+1

$$\tan Y = \dfrac{\text{XZ}}{\text{XY}} = \dfrac{\sqrt{25^2 - 24^2}}{24} = \dfrac{7}{24}$$

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Mar 9, 2019