Question

find the area of the triangle abc
( a = 11.54 ) in ( b = 6.15 ) in ( c = 13.37 ^ { circ } )
the area of the triangle is ( square ) ( mathrm { in } ^ { 2 } )
(simplify your answer. type an integer or decimal rounded to the
earest tenth as needed.)

Explanation:

Step1: Recall the formula for the area of a triangle

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

Step2: Substitute the given values into the formula

Given \(a = 11.54\), \(b=6.15\), and \(C = 13.37^{\circ}\). First, find \(\sin(13.37^{\circ})\). Using a calculator, \(\sin(13.37^{\circ})\approx0.231\). Then substitute into the formula:

$$
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Step3: Perform the calculation

$$
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Answer:

\(8.2\)