Question

find the area of the given triangle.

1. a = 46°, b = 30 ft, c = 16 ft

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle when two sides \(b\), \(c\) and the included angle \(A\) are given is \(S=\frac{1}{2}bc\sin A\).

Step2: Substitute the given values into the formula

Given \(b = 30\) ft, \(c=16\) ft, and \(A = 46^{\circ}\). We know that \(\sin(46^{\circ})\approx0.7193\).
Substitute into the formula: \(S=\frac{1}{2}\times30\times16\times\sin(46^{\circ})\).
First, calculate \(\frac{1}{2}\times30\times16 = 240\).
Then, \(S=240\times0.7193\).

Step3: Calculate the final result

\(S = 240\times0.7193=172.632\) square - feet.

Answer:

\(172.632\) square - feet.