Given:
Given that the triangle.
Let the length of the side a be 10 cm.
Let the length of the side b be 13 cm.
Let the measure of ∠C is 105°
We need to determine the area of the triangle.
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]A=\frac{1}{2} a b \ sin \ c[/tex]
Substituting a = 10, b = 13 and ∠C = 105°, we get;
[tex]A=\frac{1}{2}(10)(13) \ sin \ 105[/tex]
Simplifying, we get;
[tex]A=\frac{1}{2}(10)(13)(0.966)[/tex]
[tex]A=\frac{1}{2}(125.58)[/tex]
[tex]A=62.79 \ cm^2[/tex]
Rounding off to 1 decimal place, we have;
[tex]A=62.8 \ cm^2[/tex]
Thus, the area of the triangle is 62.8 cm²
