Sine rule

Soh Cah Toa is an efficient way to find length of sides, and angles of a triange. The only problem with it is that it will only work when the triangle is a right-angled triange. Therefore, when working with other triangles, it is neat to have another efficient method. One of them is the so called Sine Rule. It stated that:

a/sin A = b/sin B = c/sin C. (Fig. 1.0)

Lowercase letters in this formula are the labels of the sides on the given triangle. Uppercase letters are the labels of the angles of the given triangles. (Fig. 1.1)

(The sine rule, as well as the cosine rule will be present in your Mathematics Analysis ans Approaches formula booklet)

In the triangle (Fig. 1.1), A = 125° , b = 3.3 and a = 5,1. Find B, C and c.

Let us use the sine rule. 

(Sin 125)/5.1 = (Sin B)/3.3

To find Sin B, we can use cross multiplication, so rearranged it will look like:

Sin B = (Sin 125 × 3.3)/5.1 = 0.530.

To find the angle, we use the inverse sine so:

Sin-1 (0.530) = 32° 

You should remember that all the angles added up will be equal to 180. We know That one of the angles is 125 and one is 32. Those together will be 157°. 180-157 = 23°. That is angle C.

To find side c, we can use the sine rule again:

a/sin A = b/sin C

5.1/sin 125 = c/sin 23

Sin B = (Sin 23 × 5.1)/Sin 125 = 2.4.

So side c is 2.4.