A painter leans a 25 foot ladder against a house. The base of the ladder is 8 feet from the house. To the nearest tenth of a foot, how high does the ladder reach up the side of the house?

Question

Please help me do this

Answer 1

25 = the hypotenuse of a right triangle with sides 8 and h

25^2 = 8^2 + h^2 where h=height reached by the ladder

625 = 64 + h^2

h^2 = 625-64 = 561

h = sqr561 = about 23.69 feet

or another way to solve the problem, with trigonometry:

cosA = hypotenuse/adjacent side = 8/25

cosA = .32

A = about 71.34

sinA = sin71.34 = .95 = h/25

h =25(.95) = 23.69 feet

Answer 2

The ladder against the wall forms a right triangle, with the hypotenuse = 25 feet of ladder length, and the 8 foot distance from the ladder to the house being one of the legs. The height of the ladder is another leg.

Per the Pythagorean Theorem if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse:

a^2 + b^2 = c^2

Here a = 8, b = the unknown height and c = 25, so substituting

8^2 + b^2 = 25^2

b^2 = 25^2 - 8^2 = 561

so b = 23.7