Answer: 30.95 feet up
Explanation:
You can use trigonometry to find out how far up the building the ladder will reach. In this scenario, you have a right triangle formed by the ladder, the ground, and the side of the building. The ladder is the hypotenuse of the triangle, and you know the angle between the ground and the ladder (74°) and the length of the ladder (32 feet).
You can use the trigonometric function sine (sin) to calculate the height the ladder reaches on the building:
sin(angle) = opposite side / hypotenuse
In this case, the opposite side is the height the ladder reaches on the building (what you want to find), the angle is 74°, and the hypotenuse is 32 feet.
So, you have:
sin(74°) = height / 32 feet
Now, solve for the height:
height = 32 feet * sin(74°)
Using a calculator, calculate the sine of 74°:
sin(74°) ≈ 0.9659
Now, multiply:
height ≈ 32 feet * 0.9659 ≈ 30.9472 feet
So, the ladder will reach approximately 30.95 feet up the building.