Question

3. A sign company is building a sign with the dimensions shown. What is the area, in square feet, of the sign? Round to the nearest foot. Justify your answer by showing your work. (5 points)

Answer 1

Answer:

84.87sq ft

Step-by-step explanation:

Let ABC be the triangle and  AD be the perpendicular on BC such that BD=DC=7ft.

Now, it is known that $\frac{DC}{AC}=cos60^{0}$

$AC=\frac{7}{\frac{1}{2}}$

$AC=7ft$

Now, in triangle ADC, we have

$(AC)^{2}=(AD)^{2}+(DC)^{2}$

$(14)^{2}=(AD)^{2}+(7)^{2}$

$196-49=(AD)^{2}$

$AD=12.12ft$

Now, area of the triangle=$\frac{1}{2}{\times}b{\times}h$

=$\frac{1}{2}{\times}14{\times}12.12$

=$84.87sq ft$

Thus, area of the building is 84.87sq ft.