Question

area and perimeter of triangles
what is the area of triangle def? round to the nearest tenth of a square unit
trigonometric area formula: area = 1/2ab sin (c)

Explanation:

Step1: Identify the values of a, b and C

In triangle DEF, let \(a = 5\), \(b = 8\), and \(C=116^{\circ}\).

Step2: Use the trigonometric - area formula

The formula for the area of a triangle is \(A=\frac{1}{2}ab\sin(C)\). Substitute \(a = 5\), \(b = 8\), and \(C = 116^{\circ}\) into the formula. First, find \(\sin(116^{\circ})\approx0.8988\). Then \(A=\frac{1}{2}\times5\times8\times\sin(116^{\circ})\).
\[

$$\begin{align*} A&=\frac{1}{2}\times5\times8\times0.8988\\ &=20\times0.8988\\ &\approx18.0 \end{align*}$$

\]

Answer:

18.0 square units