Question

An 11-foot ramp is being used to load items to adock as shown in the diagram.dock11 feet..10 feetIf the base of the ramp is 10 feet from the dock, howtall is the dock?4 feet4.6 feet5 feet5.5 feet

Answer 1

Given the length of the ramp to be 11 feet and the base to be 10 feet from the dock

The height of the dock can be found by the Pythagorean theorem which is

`\begin{gathered} c^2=a^2+b^2 \\ \text{where c represents the hypotenuse } \\ \text{ a and b represent the other two sides} \end{gathered}`
`\begin{gathered} \text{put c =11 fe}et \\ a=10\text{ fe}et \\ b=x\text{ fe}et \end{gathered}`

Find x

`\begin{gathered} 11^2=10^2+x^2 \\ x^2=11^2-10^2 \\ x^2=121-100 \\ x^2=21 \\ x=\sqrt[]{21} \\ x=4.6\text{ fe}et \end{gathered}`

Therefore, from our calculation, the height of the dock is 4.6 feet