Question

determine the remaining sides and angles of the triangle abc.
a = 117.24°, c = 31.29°, c = 130
b = □°

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(A + B + C=180^{\circ}\).
We know \(A = 117.24^{\circ}\) and \(C = 31.29^{\circ}\).
So, \(B=180^{\circ}-(A + C)\).

Step2: Substitute the values of \(A\) and \(C\)

Substitute \(A = 117.24^{\circ}\) and \(C = 31.29^{\circ}\) into the formula for \(B\).
\(B=180^{\circ}-(117.24^{\circ}+ 31.29^{\circ})\).
First, calculate \(117.24^{\circ}+31.29^{\circ}=148.53^{\circ}\).
Then \(B = 180^{\circ}-148.53^{\circ}\).

Answer:

\(B = 31.47^{\circ}\)