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# how do you find the tangent when giving adjacent hypotenuse AND opposite

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how do you find the tangent when giving adjacent hypotenuse AND opposite

Guest Mar 9, 2017

#1
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Tan = Opposite side / Adjacent side

Guest Mar 9, 2017
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#1
+5

Tan = Opposite side / Adjacent side

Guest Mar 9, 2017
#2
+5

$$Tangent = \frac{Opposite}{Adjacent}$$

Since we already have the opposite, we need to solve for the adjacent.

Pythagoras: $$a^2 + b^2 = c^2$$

In this case: $$Opposite^2+Adjacent^2=Hypotenuse^2$$

$$Adjacent^2=Hypotenuse^2-Opposite^2$$

$$Adjacent = \sqrt{Hypotenuse^2-Opposite^2}$$

So, going back to the first equation (for tangent), we can plug in this for adjacent.

$$Tangent=\frac{Opposite}{\sqrt{Hypotenuse^2-Opposite^2}}$$

There we go! Use this equation ↑↑↑ to find tangent.

Guest Mar 9, 2017
edited by Guest  Mar 9, 2017

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