Question

find the area of the triangle described below. round to the nearest hundredth.

a = 126°, b = 17, c = 5

Explanation:

Step1: Use 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 \(A = 126^{\circ}\), \(b = 17\), \(c = 5\). First, find \(\sin(126^{\circ})\). Since \(\sin(126^{\circ})=\sin(180^{\circ}- 54^{\circ})=\sin(54^{\circ})\approx0.8090\).
Then substitute into the formula: \(S=\frac{1}{2}\times17\times5\times\sin(126^{\circ})\).

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Answer:

\(34.38\)