Question

Trigonometry

Answer 1

The area of the triangle EFG is 7.4 square units.

Explanation:

Given that the measurements of the sides of the triangle are EF = 8, EG = 8 and $m\angle E=22^{\circ}$

We need to determine the area of the triangle EFG

Area of the triangle:

The area of the triangle EFG can be determined using the formula,

$\text {Area}=\frac{1}{2} fg \sin E$

Substituting the values, we get,

$\text {Area}=\frac{1}{2} (5)(8) \sin 22^{\circ}$

Simplifying the values, we have,

$\text {Area}=\frac{1}{2}(40)(0.37)$

Multiplying, we get,

$\text {Area}=\frac{14.8}{2}$

Dividing, we get,

$\text {Area}=7.4$

Hence, the area of the triangle EFG is 7.4 square units.