A 26-ft ladder leans against a building so that the angle between the ground and the ladder is 75∘.

height = 26 sin75°

base is 26 cos75° feet from wall

23.96

To find the height the ladder reaches on the building, we can use the trigonometric function sine.

The formula is as follows:

sin(θ) = opposite/hypotenuse

In this case, the opposite side is the height the ladder reaches on the building, and the hypotenuse is the length of the ladder, which is 26 feet.

Therefore, we can rewrite the formula as:

sin(75∘) = height/26 feet

To find the height, we can rearrange the equation:

height = sin(75∘) × 26 feet

Using a calculator, we can find the sine of 75∘:

sin(75∘) ≈ 0.9659

Now we can substitute this value back into the equation:

height = 0.9659 × 26 feet

height ≈ 25.10 feet

So, the ladder reaches a height of approximately 25.10 feet on the building.

To determine the height at which the ladder reaches the building, we can use basic trigonometry. The ladder forms a right triangle with the ground and the side of the building.

Let's denote the height as x. The ladder itself acts as the hypotenuse of the right triangle, and the angle between the ground and the ladder is given as 75 degrees.

Using the trigonometric function sine (sin), we can establish the equation:

sin(75°) = x/26 ft

To solve for x, we can rearrange the equation:

x = sin(75°) * 26 ft

Now we can plug the values into a calculator to find the solution:

x ≈ 24.94 ft

Therefore, the ladder reaches a height of approximately 24.94 ft on the building.