  # Find a Missing Side Using the Sin Ratio

In this worksheet, students will use the Sin ratio to find the missing side of a triangle. Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:   #### Worksheet Overview

What do the following have in common?

A triangle, a tricycle, a triathlete, trigonometry.   Answer: The number three. There are three sides on a triangle, three wheels on a tricycle, three events in a triathlon and three ratios to learn in trigonometry.

"SOH, CAH, TOA" is something that every maths teacher has probably chanted at you.

We are going to look at Sin here and what the "SOH" means. S is for sin (which will be given as an angle)

O is for opposite side

H is the hypotenuse side

The line in the middle means divide. If we want to find the hypotenuse, cover up the H.  The formula we are left with is H = O/S

Hypotenuse = opposite divided by Sin(angle) If we want to find the opposite side, cover up the O.  The formula we are left with is O = S x H

Opposite = sin(angle) x Hypotenuse.

Let's look at some examples.

IMPORTANT NOTE: Make sure your calculator is set to degrees, otherwise the calculation will not work. You can tell you are in the right mode as a "D" should appear at the top of your calculator screen.

Example 1:

Find length x in this triangle. 1. Label the lengths of the triangle: A, O, and H

2. Work out the side you want to find. In this case, x is the hypotenuse, so we want H

3. The formula triangle shows that H = O / S

4. Substitute the angle and the length into the formula. This gives H = 12 / sin(32)

5. In your calculator type in 12 / sin(32)

Example 2

Find length x in this triangle 1. Label the lengths of the triangle: A, O, and H

2. Work out the side you want to find. In this case, x is the opposite, so we want O

3. The formula triangle shows that O = S x H

4. Substitute the angle and the length into the formula. This gives O = sin(47) x 11

5. In your calculator type in sin(47) x 11 