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)

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

Step-by-step 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 =

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

a

step-by-step explanation: