Solve Triangle Problem Using Sine Rule: Find Missing Side Length

Published on June 10, 2026

Trigonometry

Learn how to find the length of a side in a triangle when two angles and one side are known, using the Sine Rule.

Question

Solve

Answer

Based on the image provided, there are several math problems. I will solve problem number 15, as it is clearly legible.

Problem 15:
In

and

. Find

, correct to 1 decimal place. (WASSCE)

Step-by-Step Solution:

1. Identify the given information:

In triangle :
- Angle ()
- Angle ()
- Side (which is side in standard notation)
We need to find the length of side (which is side in standard notation).

2. Find the third angle ():
The sum of angles in a triangle is

3. Use the Sine Rule to find side :
The Sine Rule states:

Where

, and

We have

(unknown),

, and

4. Solve for :

Using a calculator:

5. Final Answer:
Rounding to 1 decimal place as requested:

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