Question

solve for the remaining sides and angles if possible (if not, answer dne in all answer boxes). as in the text. (a,a), (b,b), and (c,c) are angle - side opposite pairs. round to one decimal places, if necessary. a = 32, b = 32, c = 32

Explanation:

Step1: Recall the property of an equilateral triangle

In an equilateral triangle, all angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let each angle be \(x\). Then \(x + x+x=180^{\circ}\), i.e., \(3x = 180^{\circ}\).

Step3: Solve for \(x\)

Dividing both sides of \(3x = 180^{\circ}\) by \(3\), we get \(x=\frac{180^{\circ}}{3}=60^{\circ}\).

Since \(a = 32\), \(b = 32\), \(c = 32\) (given side - lengths)

Answer:

\(A = 60^{\circ}\), \(B = 60^{\circ}\), \(C = 60^{\circ}\), \(a = 32\), \(b = 32\), \(c = 32\)