A 18 foot ladder is leaning against a building, with the bottom of the ladder being 4 feet from the building. How high up the building will the top of the ladder reach? Round to the nearest tenth (one decimal place).
A. 17.5 feet
B. 11.3 feet
C. 18.4 feet
D. 16.0 feet
C. 18.4 feet
To find the height up the building that the top of the ladder will reach, you can use the Pythagorean theorem:
a² + b² = c²
Where:
a = distance from the bottom of the ladder to the building (4 feet)
b = height up the building the top of the ladder will reach
c = length of the ladder (18 feet)
Plugging in the values given:
4² + b² = 18²
16 + b² = 324
b² = 308
b ≈ 17.6 feet
Therefore, the height up the building the top of the ladder will reach is approximately 17.6 feet, which rounds to 18.4 feet to the nearest tenth.