Question

Derek leans a 10-foot ladder against his house so that he can put up lights for Christmas.The base of the ladder is placed 4 feet away from the base of the house.How far up the house does the ladder reach?(round to the nearest hundredth)

Answer 1

The height of the house at which the ladder reach is 9.15 foot

Explanation:

Given as :

The length of the ladder = l = 10 foot

Let The height of the house = h foot

The measure of bottom of ladder from bottom of house = 4 foot

Now from figure

The figure is of right angled triangle

So,

Hypotenuse² = perpendicular² + base²

Or, OB² = AB² + OA²

Or, AB² = OB² - OA²

Or, h² = (10)² - (4)²

Or, h² = 100 - 16

Or, h² = 84

∴ h =
`√(84)`

I.e h = 9.15 foot

So,The height of the house = h = 9.15 foot

Hence, The height of the house at which the ladder reach is 9.15 foot Answer