Question

Bran is standing on the top of a building of height 18 feet and is holding a long ladder of length 25 feet that is 7 feet away from the base of the building as shown below.
What is Bran’s height?

• A. 7 ft
• B. 5 ft
• C. 6 ft
• D. 4 ft

Answer 1

The correct option is C 6 ft

Height of the building = 18 ft
Length of the ladder = 25 ft
Distance between the base of the ladder and the building = 7 ft
The triangle formed is shown below:
Let’s consider $\Delta ABC$.
$B{C}^2=A{B}^2+A{C}^2$ (by Pythagorean theorem)
$\Rightarrow {25}^2=7^2+A{C}^2$ (substitute 25 for BC and 7 for AB)
$\Rightarrow 625=49+A{C}^2$
$\Rightarrow A{C}^2=625-49$
$\Rightarrow AC=\sqrt{576}$ (evaluate the powers)
$\Rightarrow AC=24$ (take the positive square for each side)
$AC=18+h$
$\Rightarrow 24=18+h$
$\Rightarrow h=6$
Bran’s height is 6 ft.
Hence, the correct answer is option B.