Question

1. A boy is standing next to a 6 ft tent.The shadow of the tent is 9 ft long andthe boy's shadow is 7.5 ft long. How tallis the boy?

Answer 1

Given:

There are given the statement:

The height of the tent is 6 ft.

The height of the shadow of the tent is 9 ft.

The height of the boy's shadow is 7.5 ft.

Step-by-step explanation:

To find the height of the boy, we need to use the tan function:

So,

`tanx=\frac{height\text{ of tent}}{height\text{ of their shadow}}=\frac{height\text{ of the boy}}{height\text{ of their shadow}}`

Then,

`(6)/(9)=(h)/(7.5)`

Then,

Solve the above expression for the value of h:

Then,

`\begin{gathered} (6)/(9)=(h)/(7.5) \\ (2)/(3)=(h)/(7.5) \\ 2(7.5)=3h \\ 15=3h \\ h=(15)/(3) \\ h=5ft \end{gathered}`

Final answer:

Hence, the height of the boy is 5 ft.