Question

find the area. round your answer to the nearest hundredth if necessary. find the area of the triangle with the following measurements: b = 67°, a = 13 cm, c = 21 cm 136.5 cm² 251.3 cm² 53.33 cm² 125.65 cm²

Explanation:

Step1: Recall the formula for the area of a triangle

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

Step2: Substitute the given values into the formula

Given \(a = 13\space\text{cm}\), \(c=21\space\text{cm}\), and \(B = 67^{\circ}\). First, find \(\sin(67^{\circ})\approx0.9205\). Then substitute into the formula:

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Answer:

\(125.65\space\text{cm}^{2}\) (the fourth option)