Solving for an Unknown Side Length Using the Law of Sines

Published on September 20, 2026

Trigonometry

Calculate the unknown side length x in a triangle using the Law of Sines given two interior angles and one opposite side length.

Question

Based on the image provided, we have a triangle with the following given information:

Step 1: Find the interior angles of the triangle.
The angle labeled

is an exterior angle to the triangle. The interior angle adjacent to it is:

Wait, looking closer at the diagram, the

angle is likely the interior angle at that vertex, and the

angle is the interior angle at the top vertex. Let’s re-examine the labels.
The angle at the top is

. The angle at the bottom right is

.
The third angle (top left) is:

Step 2: Identify the sides relative to the angles.

Step 3: Use the Law of Sines to solve for .

Step 4: Calculate the final value.
Using

and

Final Answer: