Question

A ladder is leaning against a building. The base of the ladder is 7 meters from the base of the building. If the ladder is 20 meters tall, what is the angle the ladder makes with the building? Round your answer to the nearest hundredth of a degree.

Answer 1

The angle that the ladder makes with the building can be found using trigonometry. By calculating the arccosine of the ratio of the base of the ladder to its length (7/20), we determine that the angle is approximately 69.46 degrees.

Step-by-step explanation:

To determine the angle the ladder makes with the building, you can use the trigonometric function cosine, which is given by the adjacent side divided by the hypotenuse in a right-angled triangle. In this case, the base of the ladder represents the adjacent side, and the ladder itself is the hypotenuse.

The adjacent side (base of the ladder) is 7 meters, and the hypotenuse (ladder) is 20 meters. The cosine of the angle (θ) can be calculated as follows:

cos(θ) = adjacent/hypotenuse = 7/20

To find the angle, you take the arccosine (inverse cosine) of the above ratio:

θ = arccos(7/20)

Using a calculator, this gives you:

θ ≈ arccos(0.35)

θ ≈ 69.46° (rounded to the nearest hundredth)

So, the angle the ladder makes with the building is approximately 69.46°.