Answer:
[tex]56.5ft^2[/tex]
Explanation:
We were given an isosceles triangle:
Side = 11 ft
Angle = 34.5
The sum of interior angles in a triangle is 180 degrees. This means that:
[tex]\begin{gathered} 34.5+34.5+x=180 \\ 69+x=180 \\ \text{Subtract ''69'' from both sides, we have:} \\ x=180-69 \\ x=111^{\circ} \end{gathered}[/tex]
The angle between the identical sides of the triangle is 111 degrees
The area of the isosceles triangle is given by:
[tex]\begin{gathered} Area=\frac{1}{2}s^2\sin \theta \\ s=11ft \\ \theta=111^{\circ} \\ Area=\frac{1}{2}\times11^2\times\sin 111^{\circ} \\ Area=\frac{1}{2}\times121\times0.9336 \\ Area=56.4828\approx56.5 \\ Area=56.5ft^2 \end{gathered}[/tex]
Therefore, the area of the triangle is 56.5 sq feet
