Question

find the area of the triangle abc
a = 10.8 m b = 5.1 m c = 14.5°
the area of the triangle is □ m²
(simplify your answer. type an integer or decimal rounded to the nearest 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 given is \(A=\frac{1}{2}ab\sin C\).

Step2: Substitute the given values into the formula

Here, \(a = 10.8\), \(b=5.1\), and \(C = 14.5^{\circ}\). So \(A=\frac{1}{2}\times10.8\times5.1\times\sin(14.5^{\circ})\).
First, calculate \(\frac{1}{2}\times10.8\times5.1\): \(\frac{1}{2}\times10.8\times5.1 = 27.54\).
Then, find \(\sin(14.5^{\circ})\approx0.2504\) (using a calculator).

Step3: Calculate the area

Multiply the two results: \(A = 27.54\times0.2504\approx6.9\).

Answer:

\(6.9\)