Label Sides of a Triangle

How can you find the height of this mountain?

How can this mountaineer draw an accurate map?

How did sailors navigate before GPS?

How can computers rotate images so that they can be viewed from many different directions?

Answer:

By looking at angles and sides of triangles, and making connections between them.

This is called trigonometry.

Trigonometry is concerned with calculating the sides of triangles and angles within them.

There are three important ratios that you will need to know:  sine, cosine and tangent. These are ratios of the sides of a right angled triangle, which are used for finding an angle.

Before you can solve anything using sine, cosine and tangent accurately, you need to be able to label a triangle correctly.

Things to remember

The longest side of a right angled triangle is called the hypotenuse (H)

The side opposite the angle is called the opposite side (O)

The side next to the angle is called the adjacent side (A)

Example

Label the lengths on this triangle:

Label the hypotenuse first, as it is the easiest to spot. The hypotenuse is always the longest side:

Next, look at the angle. The length that touches this angle is the adjacent:

That just leaves the opposite side to label. It is the length that is literally opposite the angle: 

Have a go at the following set of questions to test your understanding.