Question

find the area of the triangle described below. round to the nearest hundredth.
c = 129°57, a = 12, b = 14

Explanation:

Step1: Convert the angle from degrees and minutes to decimal degrees

We know that \(1^{\circ}=60'\). So, \(57'=\frac{57}{60}=0.95^{\circ}\). Then \(C = 129^{\circ}57'=129.95^{\circ}\)

Step2: Use the formula for the area of a triangle \(A=\frac{1}{2}ab\sin C\)

Substitute \(a = 12\), \(b = 14\), and \(C=129.95^{\circ}\) into the formula.
First, calculate \(\sin(129.95^{\circ})\). Using a calculator, \(\sin(129.95^{\circ})\approx0.7677\)
Then \(A=\frac{1}{2}\times12\times14\times0.7677\)
\(A = 6\times14\times0.7677\)
\(A=84\times0.7677\)
\(A = 64.4868\)

Answer:

\(64.49\)