Question

a painter is going to apply a special coating to a triangular metal plate on a new building. two sides measure 14.9 cm and 19.3 cm. she knows that the angle between the two sides is 129°. what is the area of the surface she plans to cover with the coating? the surface area is cm². (simplify your answer. type an integer or a decimal. round to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for the area of a triangle with two sides and included angle

The formula is \(A=\frac{1}{2}ab\sin C\), where \(a\) and \(b\) are the lengths of two sides and \(C\) is the included angle.
Here, \(a = 14.9\), \(b=19.3\), and \(C = 129^{\circ}\).

Step2: Substitute the values into the formula

\(A=\frac{1}{2}\times14.9\times19.3\times\sin(129^{\circ})\)
First, calculate \(\sin(129^{\circ})\approx0.777\) (using a calculator in degree - mode).
Then \(A=\frac{1}{2}\times14.9\times19.3\times0.777\)
\(A = 0.5\times14.9\times19.3\times0.777\)
\(A=7.45\times19.3\times0.777\)
\(A = 143.785\times0.777\)
\(A\approx111.7\)

Answer:

\(111.7\)