# Calculating a length

The three trigonometric ratios can be used to calculate the length of a side in a right-angled triangle.

### Example

Calculate the length AB. Give the answer to one decimal place.

Label the sides of the triangle , and .

Next choose the correct ratio from .

The length is known and the length must be calculated.

Use

Make AB the subject by multiplying both sides by 8.

AB =

AB = 4.2 cm

It may be necessary to rearrange the formula to calculate a length.

Question

Calculate the length YZ. Give the answer to one decimal place.

Label the sides of the triangle , and .

Next choose the correct ratio from .

The length is known and the length must be calculated.

Use:

Rearrange the equation to make YZ the subject.

Multiply both sides by YZ.

Divide both sides by .

YZ =

YZ = 5.0 cm