Question

Find the height of the building. Round your answer to the nearest tenth. Explain how you found your answer.

Answer 1

Given:

a = x ft

b = 40ft

c = 65ft

According to the Pythagorean Theorem, we can find the value of the hypotenuse of a right triangle through the following formula:

`a^2+b^2=c^2`
`c=\sqrt[]{a^2+b^2}`

Given that:

a = side

b = side

c = hypotenuse

With this formula, we can manipulate it ti find the value of a side instead.

`a^2+b^2=c^2`
`a^2=c^2-b^2`
`a=\sqrt[]{c^2-b^2}`

Next, we plug in the given values that we have

`a=\sqrt[]{c^2-b^2}`
`x=\sqrt[]{(65)^2-(40)^2}`

`=\sqrt[]{4225-1600}`
`=\sqrt[]{2625}`
`x=51.235`

Since the question are asking to round the answer to the nearest tenth, the final answer would be

`x=51.2\text{ ft}`