Question

1larr The base of a 13-foot ladder is 4 feet from a building. If the ladder reaches the flat roof, how tall is the building?

Answer 1

The height of the building is approximately 12.37 feet.

Step-by-step explanation:

To find the height of the building, we can use the Pythagorean theorem. The ladder forms a right triangle with the building and the ground. The ladder is the hypotenuse, and the distance from the base of the ladder to the building is one of the legs of the triangle. Using the Pythagorean theorem, we can say that the height of the building is equal to the square root of the square of the ladder length minus the square of the distance from the base to the building.

Given that the ladder length is 13 feet and the distance from the base to the building is 4 feet, we can calculate the height of the building as follows:

Height = sqrt(13² - 4²) = sqrt(169 - 16) = sqrt(153) ≈ 12.37 feet

Answer 2

The height of the building rounded to the nearest tenth is approximately 12.4 feet.

Given that, the base of a 13-foot ladder is 4 feet from a building.

The situation described forms a right-angled triangle.

Where;

Hypotenuse = 13 ft

Leg 1 = 4 ft

Leg 2 =?

To determine the length of leg 2 or the height of the building, we use the Pythagoras theorem:

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

Plug in the values:

( 13)² = ( 4 )² + ( leg 2 )²

169 = 16 + ( leg 2 )²

Leg 2 = √( 169 - 16 )

Leg 2 = √( 153 )

Leg 2 = 12.4 ft

Therefore, the building has a height of approximately 12.4 ft