Nicolas places his 30 ft ladder against his house he is painting. if the foot of the ladder is 8 ft from the base of the house, how high above the ground is the top of the ladder touching the house. nearest tenth. pythagorean’s theorem

28.9'

Step-by-step explanation:

Using the Pythagorean Theorem:

Let a = 8' base

Let b = x

Let c = 30' ladder

a^2 X b^2 = c^2

(8)^2 X (x)^2 = (30)^2

64 X (x)^2 = 900  (Subtract 64 from both sides of the equation)

x^2 = 836

x = 28.9'

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.