Question

a farmer leans a 12-ft ladder against a barn. The base of the ladder is 3 ft from the barn. To the nearest tenth, how high on the barn does the ladder reach?

Answer 1

11.6 ft

Explanation:

I attached a diagram for you to easily visualize this problem.

To solve this problem, you would use the pythagorean theorem. The 12-ft ladder is the hypotenuse and the 3 ft from the barn is one of the side legs. You want to find the length of the "other side leg", or the height of the barn.

Substitute 3, 12, and x into the pythagorean theorem like so.

a^2 + b^2 = c^2

3^2 + x^2 = 12^2

Evaluate the exponents.

9 + x^2 = 144

Subtract 9 from both sides.

x^2 = 135

Square root both sides.

x = 11.618

Round this to the nearest tenth: 11.6 feet.