Question

A ladder 31.6 feet long reaches to the top of a building when its foot stands 12.1 feet from the building. How high is the building?

Option 1: 30.5 feet
Option 2: 28.1 feet
Option 3: 29.5 feet
Option 4: 27.6 feet

Answer 1

The height of the building is calculated using the Pythagorean theorem with the ladder's length as the hypotenuse and the distance from the building as one of the legs. After solving for the height, the closest option to the calculated height of approximately 29.2 feet is Option 3: 29.5 feet.

Step-by-step explanation:

The student is faced with a problem involving a ladder, a building, and the use of the Pythagorean theorem to find the height of the building. The ladder, building, and ground form a right triangle, where the ladder represents the hypotenuse and the height of the building is one of the legs. To solve for the height of the building (let's call it 'h'), we use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The equation can be written as:

c2 = a2 + b2

Using the lengths provided:

31.62 = h2 + 12.12

h2 = 31.62 - 12.12

h2 = 998.56 - 146.41

h2 = 852.15

h = √852.15

h ≈ 29.2 feet

Since 29.2 feet is not an option provided in the question, and it is closest to Option 3: 29.5 feet, we can conclude that Option 3 is the correct answer.