Question

find the area of a triangle with the given description. (round your answer to one decimal place.) a triangle with sides of length 6 and 9 and included angle 78°

Explanation:

Step1: Recall area formula

The area formula for a triangle with two - side lengths \(a\) and \(b\) and included - angle \(\theta\) is \(A=\frac{1}{2}ab\sin\theta\). Here \(a = 6\), \(b = 9\), and \(\theta=78^{\circ}\).

Step2: Substitute values

Substitute \(a = 6\), \(b = 9\), and \(\theta = 78^{\circ}\) into the formula: \(A=\frac{1}{2}\times6\times9\times\sin(78^{\circ})\).
First, calculate \(\frac{1}{2}\times6\times9 = 27\).
Then, find \(\sin(78^{\circ})\approx0.9781\).

Step3: Calculate the area

Multiply \(27\) by \(\sin(78^{\circ})\): \(A = 27\times0.9781=26.4087\).

Step4: Round the answer

Round \(26.4087\) to one decimal place. \(A\approx26.4\).

Answer:

\(26.4\)