A ladder leans against a house at a 60° angle to the ground. If the ladder extends to a length of 166 inches, what is the height of the house to the nearest hundredth of an inch?

No idea. Does the ladder reach the roof? If so, and it does not extend beyond the edge of the roof (see how poorly posed the problem is?)

sin60° = height/length

height = 0.866 * 166 = 143.76 in.

A ladder leans against a house at a 60° angle to the ground.

House with a ladder measuring 166 inches forming a right triangle. The base angle formed by the ladder is 60 degrees.

If the ladder extends to a length of 166 inches, what is the height of the house, rounded to the nearest hundredth of an inch?

To find the height of the house, we can use the trigonometric function sine. The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the height of the house is the opposite side, and the length of the ladder is the hypotenuse.

Given that the ladder extends to a length of 166 inches and the angle between the ladder and the ground is 60 degrees, we can use the equation:

sin(60°) = height / 166

To solve for the height, we rearrange the equation:

height = sin(60°) * 166

Using a calculator, we find:

sin(60°) ≈ 0.86603

Therefore, the height of the house is approximately:

height ≈ 0.86603 * 166

Calculating this gives:

height ≈ 143.93298

To the nearest hundredth of an inch, the height of the house is approximately 143.93 inches.