The area of the triangle ABC is 207.5 square units.
Explanation:
The measurements of the sides of the triangle are [tex]AB=19[/tex], [tex]AC=24[/tex] and [tex]m\angle A=65^{\circ}[/tex]
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,
[tex]{Area}=\frac{1}{2} b c \sin A[/tex]
where [tex]b=19[/tex], [tex]c=24[/tex] and [tex]m\angle A=65^{\circ}[/tex]
Substituting these values in the above formula, we get,
[tex]{Area}=\frac{1}{2}(19)(24) \sin 65^{\circ}[/tex]
Simplifying the values, we get,
[tex]{Area}=\frac{1}{2}(456) (0.91)[/tex]
[tex]{Area}=\frac{1}{2}(414.96)[/tex]
[tex]{Area}=207.48[/tex]
Rounding off to the nearest tenth, we get,
[tex]{Area}=207.5[/tex]
Thus, the area of the triangle ABC is 207.5 square units.
Answer:
206.6 units²
Step-by-step explanation:
Area = ½ × AB × AC × sin(A)
= ½ × 19 × 24 × sin(65)
= 206.6381754444
