Question

A ladder that leans against a wall reaches a point 15 ft above the ground. The base of the ladder is 3.9 ft from the base of the wall. What is the length of the ladder?

a) 15 ft
b) 3.9 ft
c) 18.9 ft
d) Not enough information provided

Answer 1

The length of the ladder is
`\( √(15^2 + 3.9^2) \)`, which is approximately 15.5 ft. So, Option A is correct.

Step-by-step explanation:

The problem involves a right-angled triangle formed by the ladder, the wall, and the ground. The ladder acts as the hypotenuse, the wall as one leg, and the ground as the other leg. 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), can be used to find the length of the ladder.

The Pythagorean theorem is given by
`\(c^2 = a^2 + b^2\)`, where c is the length of the ladder, a is the distance from the base of the ladder to the wall, and b is the height the ladder reaches above the ground. In this case,
`\(c^2 = 15^2 + 3.9^2\)`. Solving for c, we get
`\(c \approx √(15^2 + 3.9^2) \)`, which simplifies to approximately 15.5 ft.

Therefore, the length of the ladder is approximately 15.5 ft. This calculation accounts for the vertical height the ladder reaches and the horizontal distance from the base of the ladder to the wall. The Pythagorean theorem is a fundamental principle in geometry and is widely used to solve problems involving right-angled triangles.