Question

Kristos is using a 14-foot ladder to reach an attic vent on the side of his house. He places the ladder 4 feet from the base of the house and leans it against the house until it just touches the vent.

What is the height of the attic vent?

A. 10.0 feet B. 13.4 feet
C. 14.6 feet D. 18.0 feet

Answer 1

The height of the attic vent is approximately 13.4 feet.

Step-by-step explanation:

To find the height of the attic vent, we can use the concepts of similar triangles. The ladder forms a right triangle with the ground and the house. The height of the attic vent is represented by the height of the ladder against the house.

Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the height of the attic vent as follows:

1. The base of the ladder is 4 feet.
2. The length of the ladder is 14 feet.
3. Let h be the height of the attic vent.
4. Applying the Pythagorean theorem, we have: 4^2 + h^2 = 14^2.
5. Simplifying the equation, we get: 16 + h^2 = 196.
6. Subtracting 16 from both sides, we have: h^2 = 180.
7. Taking the square root of both sides, we find: h = sqrt(180).
8. Approximating the value, we get: h ≈ 13.416 ft.

Therefore, the height of the attic vent is approximately 13.4 feet.

Answer 2

the answer is 18.0 feet!!