How to find the length of the hypotenuse of an acute / obtuse triangle

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ACT Math › How to find the length of the hypotenuse of an acute / obtuse triangle

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What is the value of in the triangle above? Round to the nearest hundredth.

Cannot be calculated

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

_tri12

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

$\frac{sin(30)}{30}=\frac{sin(100)}{x}$

Solving for , you get:

$x=\frac{30sin(100)}{sin(30)}=59.0884651807326...$

Rounding, this is .