Question

1. find the length of each side.

3x + 21
54
x + 15

Explanation:

Step1: Apply the Law of Sines

Since the angles are equal (the triangle has two equal angles, so it is isosceles), the sides opposite these angles are equal. So, \(3x + 21=x + 15+54\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(3x - x+21=x - x+15 + 54\), which simplifies to \(2x+21 = 69\).
Subtract 21 from both sides: \(2x+21-21=69 - 21\), so \(2x=48\).
Divide both sides by 2: \(x = 24\).

Step3: Find the lengths of the sides

For \(x + 15\): Substitute \(x = 24\), we get \(24+15=39\).
For \(3x + 21\): Substitute \(x = 24\), \(3\times24+21=72 + 21=93\).

Answer:

The lengths of the sides are \(39\), \(54\), and \(93\).