Respuesta :
To calculate the area of a triangle with two sides given and the angle opposite the third side, we shall apply the following formula;
[tex]\begin{gathered} \text{Area}=ab\times\frac{\sin C}{2} \\ \text{Where} \\ a=\text{side,b}=\text{side,C}=\text{angle} \end{gathered}[/tex]The triangle is an isosceles triangle, which mean sides a and b both measure 17.91 ft each and angle C = 21.21 degrees.
Therefore, the area would be;
[tex]\begin{gathered} \text{Area}=17.91\times17.91\times\frac{\sin 21.21}{2} \\ \text{Area}=320.7681\times\frac{0.361787285773668}{2} \\ \text{Area}=320.7681\times0.180893642886834 \\ \text{Area}=58.023625\ldots \\ \text{Area}\approx58.024ft^2\text{ (rounded up to the nearest thousandth)} \end{gathered}[/tex]The correct answer therefore is option C, which is 58.025 sq ft.
This is the closest we got from our calculation which is as a result of approximations
