How can I find the two missing side-lengths of a right triangle if I just know one side-length and one angle measure, not counting the ninety degree angle?

Question

anonymous · Answer

I know that you use sin/cos/tan, but I would like a more elaborate explanaton

jim_thompson5910 · Answer

say we have this triangle with this given known angle

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jim_thompson5910 · Answer

and say we also know that the opposite leg is 5 units and the hypotenuse is unknown (so it's x units long at this point)

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anonymous · Answer

Ok I'm following

jim_thompson5910 · Answer

we can then use the sine function

sin(angle) = opposite/hypotenuse

sin(30) = 5/x

now solve for x

sin(30) = 5/x

0.5 = 5/x ... use a unit circle or a calculator to find sin(30) = 0.5

0.5*x = 5

x = 5/0.5

x = 10

So if we know that the opposite leg of the 30 degree angle is 5 units, then we can figure out the hypotenuse of the right triangle to be 10 units long

jim_thompson5910 · Answer

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