Question

The distance between the two buildings is 15 feet. One building is 120 feet tall, and the other building is 128 feet. What is the distance between the top of the two buildings?

• A. 17 ft
• B. 23 ft
• C. 19 ft
• D. 7 ft

Answer 1

The correct option is A 17 ft

Height of the first building = 128 ft
Height of the second building = 120 ft
Distance between the two buildings = 15 ft
The difference between the height of the two buildings = $128-120=8ft$
The triangle formed between the two buildings is shown below.

Distance between the top of the two buildings is equal to the hypotenuse of the triangle.
$A{C}^2=A{B}^2+B{C}^2$
$\Rightarrow A{C}^2={15}^2+8^2$ (substitute 15 for AB and 8 for BC)
$\Rightarrow A{C}^2=225+64$
$\Rightarrow AC=\sqrt{289}$ (evaluate the powers)
$\Rightarrow AC=17$ (take the positive square for each side)
The distance between the top of the two buildings is 17 ft.
Hence, the correct answer is option B.