Question

1. a 26-foot board is leaning against a wall. it is set 10 feet from the base of the wall.

how far up the wall does the board reach?
28 feet
36 feet
24 feet
16 feet
clear all

Explanation:

Step1: Define Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c$ = hypotenuse, $a,b$ = legs.

Step2: Assign values to variables

Let $c=26$ ft (board), $a=10$ ft (distance from wall), $b$ = height on wall.

Step3: Rearrange to solve for $b$

$b = \sqrt{c^2 - a^2}$

Step4: Substitute and calculate

$b = \sqrt{26^2 - 10^2} = \sqrt{676 - 100} = \sqrt{576} = 24$

Answer:

C. 24 feet