Advanced trig. Calculating a side length with The Sine rule

To find a missing side in a non right angled triangle you can use the sine rule or cosine rule. In this article I will find a missing side using the sine rule. In order to do this you must be given the angle opposite the side you are finding and another side opposite an angle. The formula for the Sine rule is a/sinA = b/sinB. The small letters are the sides and the big letter are the angles. Notice that the sides are on the numerators when you are calculating a missing side length.

Question 1 (using the sine rule to find a missing side)

Calculate the missing side (x).

To begin with label your triangle. Call the side that you are trying to find small a, and the angle opposite this side A. Therefore, the other side will be called small b and the other angle can be called big B. (the side that you are finding should always be labelled small a)

Make sure you have labelled your triangle correctly before substituting your values into your sine rule.

Now you can plug your numbers into your formula:

a/sinA = b/sinB

x/sin(108)= 61/sin(33)

Now since is x is being divided by sin108 multiply the right hand side of the equation by sin 108.

This will give you:

x= 61/sin33 × sin108

x= 107mm to the nearest mm.

Extra tips using the sine rule:

Think of 2 pairs when using the sine rule. One pair is the side you are finding opposite a given angle. The second pair is the other given side and angle.

Always label the side you finding small a.

For another example on using the sine rule click here.

For some contextual questions on using the sine rule click here.