Question

A painter places an 11-ft ladder against a house. The base of the ladder is 3 ft from the house. How high on the house does the ladder reach?

Answer 1

use Pythagoras theorem
11^2 = h^2 + 3^2 where h is the height of ladder agaianst the wall

h^2 = 11^2 - 3^2
=(11+3)(11-3) = 14 * 8 = 112
h = sqrt 112 = 10.58 ft

Answer 2

The ladder reach 10.58 feet

Explanation:

In this problem a rectangle triangle is formed, with hypotenuse = 11 feet, a side = 3 feet and the other side is the unknown, i. e., how high on the house the ladder reach.

From Pythagorean theorem:

hypotenuse^2 = side^2 + side^2

11^2 = 3^2 + side^2

side^2 = 11^2 - 3^2

side = sqrt(112)

side = 10.58 feet