Question

A 17-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?

Answer 1

13.75 ft (nearest hundredth)

Explanation:

The ladder creates a right triangle with the wall and ground, where:

• leg (base) = ground
• leg (height) = wall
• hypotenuse = ladder

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

• a = 10 ft
• c = 17 ft

Substitute the given values into the formula and solve for b:

⇒ 10² + b² = 17²

⇒ b² = 17² - 10²

⇒ b² = 289 - 100

⇒ b² = 189

⇒ b = ±√(189)

As distance is positive, b = √(189) ft only

Therefore, the ladder reaches 13.75 ft (nearest hundredth) up the wall.

Answer 2

13.747... meters

Explanation:

Refer to image attached~

• Let AC represent the length of the ladder.
• Let BC represent the distance from the base of the ladder from the base of the building.
• Let AB (x) represent the height of the building.

In this case, the longest side of the triangle formed is AC. Thus, our hypotenuse is AC (17 m).

To determine the height of the building, we need to use pythogoras theorem.

Pythogoras theorem: (Hypotenuse)² = (Side)² + (Side)²

• ⇒ (17)² = (10)² + (x)²
• ⇒ 289 = 100 + (x)²
• ⇒ 289 - 100 = (x)²
• ⇒ 189 = (x)²

Take square root both sides:

• ⇒ √189 = √(x)²
• ⇒ x = √189 ≈ 13.747... meters