Question

find the area of a triangle with sides of length 7 and 8 and included angle 68°.

Explanation:

Step1: Recall the area - formula for a triangle

The formula for the area of a triangle with two - side lengths \(a\) and \(b\) and the included angle \(\theta\) is \(A=\frac{1}{2}ab\sin\theta\).

Step2: Identify the values of \(a\), \(b\), and \(\theta\)

Here, \(a = 7\), \(b = 8\), and \(\theta=68^{\circ}\).

Step3: Calculate the area

We know that \(\sin68^{\circ}\approx0.9272\). Then \(A=\frac{1}{2}\times7\times8\times\sin68^{\circ}\). First, \(\frac{1}{2}\times7\times8 = 28\). Then \(A = 28\times\sin68^{\circ}\approx28\times0.9272 = 25.9616\).

Answer:

\(A\approx25.96\)