Question

fall 2025 geometry 8 wwva area and perimeter of triangles what is the area of △abc? round to the nearest tenth of a square unit. trigonometric area formula: area = \\(\frac{1}{2}ab\sin(c)\\)

Explanation:

Step1: Identify the formula and values

The formula for the area of a triangle is $A=\frac{1}{2}ab\sin(C)$. Here $a = 2\sqrt{2}$, $b = 6$, and $C=80^{\circ}$.

Step2: Calculate the area

First, find $\sin(80^{\circ})\approx0.9848$. Then $A=\frac{1}{2}\times2\sqrt{2}\times6\times\sin(80^{\circ})$. Substitute the values: $A = \sqrt{2}\times6\times0.9848\approx1.414\times6\times0.9848=1.414\times5.9088\approx8.35\approx8.4$.

Answer:

8.4 square units