Question

Solar panels installed in a backyard have a cross section that is a right triangle. The diagram shows the approximate dimensionsof this cross section. A vertical support from the right angle to the ground is recommended. Approximate the length of thesupport to the nearest tenth of a foot.13.6ft4.4ft14.3ft

Answer 1

Answer:

About 4.2 ft

Explanation:

The area of the traingle can be calculated in two ways.

$A=\frac{1}{2}\text{width}\cdot\text{length}$

where width = 4.4 ft and length = 13.6 ft.

Putting in the values for width and length gives

$\begin{gathered} A=\frac{1}{2}13.6\cdot4.4_{} \\ \boxed{A=29.92ft^2} \end{gathered}$

The other way that the area can be calculated is

$A=\frac{1}{2}\cdot\text{height}\cdot\text{base}$

where height = vertical length and base = 14.3 ft; therefore.

$\begin{gathered} A=\frac{1}{2}14.3h \\ A=7.15h \end{gathered}$

This must equal the area of the triangle we found above; therefore,

$A=29.92=7.15h$$29.92=7.15h$

dividing both sides by 7.15 gives

$h=\frac{29.92}{7.15}$$\boxed{h\approx4.2ft}$

which is our answer!