Question

Trigonometry

Answer 1

The area of the triangle ABC is 154.6 square units

Explanation:

Given that the measurements of the sides of the triangles are $AB=21$ , $AC=16$ and $m\angle A=67^{\circ}$

We need to determine the area of the triangle ABC

Area of triangle ABC:

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

$\text {Area}=\frac{1}{2} b c \sin A$

Substituting the values, we get,

$\text {Area}=\frac{1}{2}(21)(16) \sin 67^{\circ}$

Simplifying the terms, we get,

$\text {Area}=\frac{1}{2}(21)(16) (0.92)$

Multiplying the values, we have,

$\text {Area}=\frac{309.12}{2}$

Dividing, we get,

$\text {Area}=154.56$

Rounding off to the nearest tenth, we get,

$Area = 154.6$

Thus, the area of the triangle ABC is 154.6 square units