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Finding missing lengths in a triangle

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Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

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Explainer Video

Tutor: Bilal

Summary

Finding missing lengths in a triangle

In a nutshell

To calculate a missing length in a triangle, you can use one of the three trigonometric ratios. The length of another side and an angle other than the right angle has to be provided.

Calculating a length in a triangle

PROCEDURE

1.	Label the sides and angle of the triangle.
2.	Work out what trigonometric ratio you have to use (SOH, CAH or TOA).
3.	Write down and rearrange the formula to make your missing side the subject.
4.	Substitute in your values for the other side and the angle to get the length.

Example 1

Find the value of the side labelled $x$ in the diagram given to 1 decimal place.

Maths; Trigonometry; KS3 Year 7; Finding missing lengths in a triangle

Label the sides and angle:

$O$  and $H$ are the given sides. So, use SOH:

$\sin(50) = \frac{O}{H}$

So:

$O = H \times \sin(50)$

Substitute the values:

$x = 10 \times \sin(50) = 7.660444....$

Round to 1 decimal place, like the question asks:

$\underline{x=7.7 \ m \ (1 \ d.p.)}$

Learn with Basics

Length:

Unit 1

Constructing triangles

Unit 2

Trigonometric ratios: SOH CAH TOA

Jump Ahead

Optional

Unit 3

Finding missing lengths in a triangle

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do I know which trigonometric ratio to use?

Label your triangle, then see what side you're given and what side you have to find and then check for the corresponding trigonometric ratio.

When do I need to use trigonometry to find the missing length?

If you're given an angle and only 1 side, then you have to use the trigonometric ratios.