Question

Trigonometry

Answer 1

The area of the triangle ABC is 207.5 square units.

Explanation:

The measurements of the sides of the triangle are $AB=19$, $AC=24$ and $m\angle A=65^{\circ}$

We need to determine the area of the triangle ABC.

Area of the triangle:

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

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

where $b=19$, $c=24$ and $m\angle A=65^{\circ}$

Substituting these values in the above formula, we get,

${Area}=\frac{1}{2}(19)(24) \sin 65^{\circ}$

Simplifying the values, we get,

${Area}=\frac{1}{2}(456) (0.91)$

${Area}=\frac{1}{2}(414.96)$

${Area}=207.48$

Rounding off to the nearest tenth, we get,

${Area}=207.5$

Thus, the area of the triangle ABC is 207.5 square units.

Answer 2

Answer:

206.6 units²

Step-by-step explanation:

Area = ½ × AB × AC × sin(A)

= ½ × 19 × 24 × sin(65)

= 206.6381754444