# How do you find the smallest angle in a right angled triangle whose side lengths are 6cm, 13cm and 14 cm?

##### 2 Answers

The smallest angle is

#### Explanation:

Since the smallest angle is always opposite the shortest side, we will solve for the value of angle A using the Law of Cosine

#### Explanation:

Sketch taken from Brian M's answer.

The Cosine Rule can be written in two ways: one for finding a side, and the transposed formula for finding an angle.

It Really is worth learning both Forms!

For side BC:

For angle A:

The smallest angle is always opposite the shortest side, so we need to find the size of Angle A in this case.

Substitute the given values:

There is little point in doing long-hand calculations, or even calculating the individual answers. It it the final value that we need.

Use a calculator, making sure to divide the whole of the numerator by the whole of the denominator. (Use brackets to ensure this.)