Question

Suppose you are standing near a bridge and you want to know its height. The bridge casts a 105-foot shadow, while you cast a 7-foot shadow

Answer 1

Given:

Shadow of the bridge = 105ft

Shadow of you = 7 ft

(a) Draw this scenario out:

(b)

`\begin{gathered} Given\text{ that you bare 5}^18^(11)\text{ tall, how tall is the bridge?} \\ Convert\text{ 5}^18^(11)\text{ to foot} \\ 5^18^(11)=5+(8)/(12)=5(2)/(3)\text{ ft} \end{gathered}`
`\begin{gathered} Let\text{ H represent height of building} \\ Using\text{ knowledge of similar triangle, } \\ (5(2)/(3))/(H)=(7)/(105) \\ \\ H=\frac{105\text{ x 5}(2)/(3)}{7} \\ H=85\text{ ft} \end{gathered}`

The bridge is 85ft tall

(c) Let the shadow of the nearby fence be x

`\begin{gathered} (8)/(85)=(x)/(105) \\ \\ x=(8(105))/(85) \\ x=9.88\text{ ft} \end{gathered}`

The length of the shadow of the nearby fence = 9.88 ft (2 decimal places)