Question

3 multiple choice 1 point find the area. round your answer to the nearest hundredth if necessary. find the area of the triangle with the following measurements: c = 102°, a = 1.7 in., b = 4.7 in. 7.82 in.² 3.91 in.² 3.995 in.² 0.83 in.²

Explanation:

Step1: Recall the formula for the area of a triangle

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

Step2: Substitute the given values into the formula

Given \(a = 1.7\) in, \(b=4.7\) in, \(C = 102^{\circ}\). First, find \(\sin(102^{\circ})\approx0.9781\). Then substitute into the formula:

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Answer:

B. \(3.91\ \text{in}^2\)