A right triangle is a triangle in which one of the angle measures 90º. In Trigonometry, there are two special right triangles one being the 45º-45º-90º right triangle and the other being 30º-60º-90º right triangle. The reason why they are called the special right triangles is because of the fact that when these angles are written with trigonometric functionssuch as sin(x), cos(x) and tan(x) where ‘x’ is the angle of the special right triangle, then exact answers are produced instead of decimal approximations.
Example 1: The side AC is the hypotenuse in the right triangle ABC. If the measure of side AC is 6m, then what is the measure of the side AB if measure of angle C is 30º?
Here triangle ABC is a special triangle because one of its angle measures 30º which implies that the angles
of the triangle are in the form of 30º-60º-90º.
The trigonometric function, sin(C) = (opposite side)/ (hypotenuse) = AB/AC
This gives: sin(30)= AB/ 6==>1/2= AB/ 6==> AB= 6 * 1/2
Therefore the measure of the side, AB= 3m
Example 2: The side PR is the hypotenuse in the right triangle PQR. If the measure of side PQ is 5m, then what is the measure of the side QRif measure of angle R is 45º?
Here triangle PQR is a special triangle because one of its angle measures 45º which implies that the angles
of the triangle are in the form of 45º-45º-90º.
The trigonometric function, tan(R) = (opposite side)/ (adjacent side)= PQ/QR
This gives: tan(45)= 5/ QR==>1= 5/ QR==>QR= 1* 5
Therefore the measure of the side, QR= 5m