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

About 4.2 ft

Step-by-step explanation:

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

`A=(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=(1)/(2)13.6\cdot4.4_{} \\ \boxed{A=29.92ft^2} \end{gathered}`

The other way that the area can be calculated is

`A=(1)/(2)\cdot\text{height}\cdot\text{base}`

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

`\begin{gathered} A=(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=(29.92)/(7.15)`
`\boxed{h\approx4.2ft}`

which is our answer!