A ladder 7.65 m long leans against the side of a building. If the ladder is inclined at an angle of 60.5° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

d = 7.65*cos60.5 = 3.77 m.

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To find the horizontal distance from the bottom of the ladder to the building, we can use the trigonometric function cosine. Here's how you can do it step by step:

Step 1: Understand the problem.
A ladder is leaning against a building, forming an angle of 60.5° with the horizontal. The ladder's length is 7.65 m. We need to find the horizontal distance from the bottom of the ladder to the building.

Step 2: Identify the relevant trigonometric function.
Since we want to find the horizontal distance, which is the side adjacent to the given angle, we will use the cosine function.

cos(angle) = adjacent/hypotenuse

Step 3: Plug in the values.
In this case, the adjacent side is the horizontal distance we want to find, and the hypotenuse is the length of the ladder.

cos(60.5°) = adjacent/7.65m

Step 4: Solve the equation.
Use the inverse cosine function (cos⁻¹) to isolate the adjacent side (horizontal distance).

adjacent = 7.65m * cos(60.5°)

Step 5: Calculate the answer.
Input the values into a calculator or use a trigonometric table to find the cosine of 60.5°, then multiply it by 7.65m to find the horizontal distance.

adjacent = 7.65m * 0.532830775

The horizontal distance from the bottom of the ladder to the building is approximately 4.08 meters.