The area of the triangle ABC is 29.61 cm²
Explanation:
The measurements of the sides of the triangle are [tex]b=9 \ cm[/tex] , [tex]c=7 \ cm[/tex] and [tex]m \angle A=70^{\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} {bc} \ sin \ {A}[/tex]
Substituting the values [tex]b=9 \ cm[/tex] , [tex]c=7 \ cm[/tex] and [tex]m \angle A=70^{\circ}[/tex], we get,
[tex]{ Area }=\frac{1}{2}(9)(7) \ sin \ {70^{\circ}}[/tex]
Simplifying the values, we have,
[tex]{ Area }=\frac{1}{2}(63) (0.94)[/tex]
[tex]{ Area }=\frac{1}{2}(59.22)[/tex]
[tex]{ Area }=29.61 \ cm^2[/tex]
Thus, the approximate area is 29.61 cm²
The area of the triangle ABC is 29.61 cm²
