Question

TRIGONOMETRY Find the area of this isosceles triangle round to the nearest tenth

Answer 1

`56.5ft^2`

Step-by-step 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:

`\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}`

The angle between the identical sides of the triangle is 111 degrees

The area of the isosceles triangle is given by:

`\begin{gathered} Area=(1)/(2)s^2\sin \theta \\ s=11ft \\ \theta=111^(\circ) \\ Area=(1)/(2)*11^2*\sin 111^(\circ) \\ Area=(1)/(2)*121*0.9336 \\ Area=56.4828\approx56.5 \\ Area=56.5ft^2 \end{gathered}`

Therefore, the area of the triangle is 56.5 sq feet