Question

1. find the area of a triangle with the following measurements: a = 42°, b = 15 m, and c = 19 m.

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 known is \(S=\frac{1}{2}bc\sin A\)

Step2: Substitute the given values into the formula

Given \(b = 15\space m\), \(c=19\space m\), \(A = 42^{\circ}\), and \(\sin42^{\circ}\approx0.6691\)

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Step3: Calculate the value

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Answer:

The area of the triangle is approximately \(95.4\space m^{2}\)