SOLUTION: how do i find the value of x in a special triangle if i only have an angle and the hypotenuse

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Question 535996: how do i find the value of x in a special triangle if i only have an angle and the hypotenuse
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle that has a hypotenuse is a right triangle, and the trigonometric ratios hold true.
Whether the right triangle is special or not, you can use the trigonometric ratios (sine, cosine, and tangent) to find the other sides.
sin%28angle%29=oppositeside%2Fhypotenuse <---> oppositeside=hypotenuse%2Asin%28angle%29
cos%28angle%29=adjacentside%2Fhypotenuse <---> adjacentside=hypotenuse%2Acos%28angle%29
You can find the values of sine, cosine, and tangent of any angle from most calculators. When the dinosaurs and I went to school, we had to look them up in tables.
Now, there are some special triangles that we know and love so much that we know the sine and cosine of their angles without looking them up.
There is the 30-60-90 right triangle that is half of an equilateral triangle. As it is half, the short side, opposite the half-angle measuring 30 degrees is half of the hypotenuse, which is a whole side of the halved right triangle. From that we know that sin+%2830%29=1%2F2
Using Pythagoras theorem we find the length of the other side and know that cos+%2830%29=sqrt%283%29%2F2, which is about 0.866.
There is also the 45-45-90 triangle that is half of a square. using Pythagoras theorem we figure out that if the hypotenuse length was 2, the length of the other two equal length sides would be sqrt%282%29.
From that we know that sin%2845%29=cos%2845%29=sqrt%282%29%2F2 and we remember that's about 0.707.