Question

a 20 foot ladder rests against a building 15 feet from the floor. how far does the ladder extend from the base wall? what angle does the ladder make with the ground?

Answer 1

angle is obviously cos inverse 15/20
height from floor=5*sqrt7

Answer 2

use pythagoras theorem

Answer 3

Recognise firstly that you're making a right-angled triangle, with the hypotenuse being the ladder; and the wall and ground making up the other two sides. One vertical side is 15 ft long, the hypotenuse is 20 ft long. Use Pythagoras' Theorem to solve for the length of the remaining side: \[a^{2} + b^{2} = c^{2}\]\[15^{2} + b^{2} = 20^{2}\]\[b^{2} = 400 - 225\]\[b^{2} = 175\]\[b = \sqrt{175} = 13.22 ft\] To get the angle the ladder makes to the ground, use the trigonometric functions - sine in this case: \[sin\theta = \frac{opposite}{hypotenuse}\]\[sin\theta = \frac{15}{20}\]\[\theta = sin^{-1}(0.75)\]\[\theta = 0.848 \: radians (48.5 \: degrees)\]