1. Introduction.
To find the missing angles and sides of a right angled triangle we can apply trigonometric ratios SOH CAH TOA. However to find the missing sides and angles of other triangles we apply sine rule. Let us learn about sine rule.
1.1 What is the Sine Rule?
The sine rule is a relationship between the size of an angle in a triangle and the opposing side. Sine rule helps in finding any missing side or angle of a triangle. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle.
Sine Rule:
It depends on the missing angle and the sides of the triangle which two of them of sine rule to be used. For example in the triangle below, b/Sin B = c/Sin C are used to find missing side c.
Note: Angles are denoted with Capital letters, while sides with lower case.
1.2 How to use the sine rule?
In order to apply the Sine rule, first label the missing sides and angles. The opposite angle is the same letter as the opposite side. Next apply the sine rule to find the missing side or angle.
While solving using the sine rule one can rewrite the formula based on the question. For example, to find missing length apply the same formula. But for finding missing angle, you can use the version where angles are in numerator.,
Sin A/a = Sin B/b = Sin C/c
Remember that each fraction in the Sine Rule formula should contain a side and its opposite angle.
Example 1: Finding a missing side of a triangle
In the given triangle Side AC = 6 cm, angle ABC = 60° and angle ACB =70°. Calculate the side AB.
Solution:
Example 2: Finding a missing angle of a triangle
In the given triangle sides, a = 8 cm, b = 6 cm, and c = 2 cm and angle ACB= 10°. Calculate angle BAC
Solution:
Example 3:
In triangle ABC, B = 21◦ , C = 46◦ and AB = 9cm. Solve this triangle for side AC
Solution:
