Question

a 65-foot ladder is placed 25 feet from a building as shown in the picture below. use the pythagorean theorem, ( a^2 + b^2 = c^2 ), where ( c ) is the height of the ladder or the hypotenuse. what is the height of the ladder from the ground?
image of a ladder leaning against a building with height h, ladder length 65 ft, and distance from building 25 ft
a 40 ft.
b 48 ft.
c 60 ft.
d 70 ft.
e 80 ft.

Explanation:

Step1: Identify known values

We know \( c = 65 \) (ladder length, hypotenuse) and \( b = 25 \) (distance from building). Let \( a = h \) (height we need to find). The Pythagorean theorem is \( a^2 + b^2 = c^2 \).

Step2: Rearrange formula to solve for \( a \)

Rearrange the formula: \( a^2 = c^2 - b^2 \). Substitute \( c = 65 \) and \( b = 25 \): \( a^2 = 65^2 - 25^2 \).

Step3: Calculate \( 65^2 - 25^2 \)

Using difference of squares: \( 65^2 - 25^2=(65 - 25)(65 + 25)=40\times90 = 3600 \). So \( a^2 = 3600 \).

Step4: Find \( a \)

Take square root: \( a=\sqrt{3600}=60 \).

Answer:

C. 60 ft.