Trigonometry

Tangent Ratio

Theory:

The tangent ratio can be used to calculate the length of one of the shorter sides (legs) of a right triangle. To do this you need the tangent ratio for one of the smaller angles, and the length of one leg of the triangle.

There are two types of these problems, depending on whether you are finding the ‘opposite’ or ‘adjacent’ side.

Finding the Opposite

Find the red side using the Tan ratio.

Tan 35= Opposite/Adjacent

tan 35= x/10

∴ x=10 x tan 35

=7.00

Tan=Opposite/Adjacent

Finding the Adjacent

Find the red side using the Tan ratio.

Tan 40= Opposite/Adjacent

tan 40= 10/x

∴ 7 = x x tan 40

7/ tan 40= x

=8.34

Adjacent=Tan/Opposite

Cosine Ratio

Theory:

The cosine ratio can be used to calculate the length of one of the shorter sides (legs) of a right triangle or to find the length of the hypotenuse. In both cases, you need to know the cosine ratio for one of the smaller angles. If you are finding an unknown leg length, then the hypotenuse must be known. If you are finding the hypotenuse, then one leg of the triangle must be known. The steps for both problem types are shown below:

Finding the Adjacent

Find the red side using the Cos ratio.

Cos 60= Adjacent/Hypotenuse

cos 60= x/20

∴ x=20 x cos 60

=10.0

Finding the Hypotenuse

Find the red side using the Cos ratio.

Cos 35= Adjacent/Hypotenuse

cos 35= 8/x

∴ cos 35 x x = 8

x=8/cos35

=9.77

Sine Ratio

Theory:

The sine ratio can be used to calculate the length of one of the shorter sides (legs) of a right triangle, or to find the length of the hypotenuse. In both cases you need to know the sine ratio for one of the smaller angles. If you are finding an unknown leg length, then the hypotenuse must be known. If you are finding the hypotenuse, then one leg of the triangle must be known. The steps for both problem types are shown below: