Question

find the area of the triangle using the following information. round to the nearest hundredth, if necessary. a = 135°, b = 18, c = 15

Explanation:

Step1: Recall the area formula

The area formula for a triangle with two - side lengths \(b\), \(c\) and included angle \(A\) is \(K=\frac{1}{2}bc\sin A\).

Step2: Substitute the given values

We are given \(A = 135^{\circ}\), \(b = 18\), and \(c = 15\). First, find the value of \(\sin A=\sin135^{\circ}=\frac{\sqrt{2}}{2}\). Then substitute into the formula:

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Step3: Calculate the numerical value

$$K\approx67.5\times1.414214 = 95.46$$

Answer:

\(95.46\)