The area of the triangle ABC is 154.6 square units
Explanation:
Given that the measurements of the sides of the triangles are [tex]AB=21[/tex] , [tex]AC=16[/tex] and [tex]m\angle A=67^{\circ}[/tex]
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,
[tex]\text {Area}=\frac{1}{2} b c \sin A[/tex]
Substituting the values, we get,
[tex]\text {Area}=\frac{1}{2}(21)(16) \sin 67^{\circ}[/tex]
Simplifying the terms, we get,
[tex]\text {Area}=\frac{1}{2}(21)(16) (0.92)[/tex]
Multiplying the values, we have,
[tex]\text {Area}=\frac{309.12}{2}[/tex]
Dividing, we get,
[tex]\text {Area}=154.56[/tex]
Rounding off to the nearest tenth, we get,
[tex]Area = 154.6[/tex]
Thus, the area of the triangle ABC is 154.6 square units
