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:

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

$O$  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:

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