Right Triangle Trigonometry

Right triangles have one 90° angle. Here, there is an angle and its corresponding opposite and adjeacent side. The hypotenuse is always the side opposite of the right angle.

Right triangles, their angles, and their sides, can be solved using a set of ratios. Just remember:

SOH CAH TOA

This acronym stands for the ratios:

SOH: sin = opposite side length ÷ hypotenuse length
CAH: cos = adjacent side length ÷ hypotenuse length
TOA: tan = opposite side length ÷ adjacent side length
So, given the following triangle, find the side lengths:

Since we know the angle, and we know one side, we can solve the rest of the triangle.

Since sin = opposite side length ÷ hypotenuse length, we can set up the equation:

sin50° = x ÷ 15
sin50° * 15 = x
x =~ 11.49
Now we can solve the third side in several different ways. You can use the pythagorean theorem (a^2+b^2=c^2), you can use the cosine of 50°, or even the tangent of 50°. Let's solve using the cosine:
cos50° = x / 15
cos50° * 15 = x
x =~ 9.64

So now we have all three side lengths:

Think you got it? Try the test!
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