A 13-ft ladder leans against a building so that the angle between the ground and the ladder is 63 degrees.

How high does the ladder reach on the building? (round your answer to the nearest foot)

sin63 = h/13, h = ?

To find how high the ladder reaches on the building, we can use trigonometry.

We have a right triangle formed by the ladder, the ground, and the building. The length of the ladder is the hypotenuse, and the height we want to find is the opposite side.

Using the sine function, we can write:

sin(63°) = opposite / hypotenuse

To find the opposite side (height), we can rearrange the equation:

opposite = sin(63°) * hypotenuse

Given that the hypotenuse (length of the ladder) is 13 ft, we can substitute the values:

opposite = sin(63°) * 13 ft

Calculating this, we get:

opposite ≈ 11.27 ft

So the ladder reaches approximately 11.27 ft high on the building. Rounded to the nearest foot, the ladder reaches 11 ft high on the building.

To find out how high the ladder reaches on the building, we can use trigonometric ratios. In this case, we can use the sine function.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this scenario, the opposite side is the height of the ladder on the building, and the hypotenuse is the length of the ladder itself.

Since we know the angle between the ladder and the ground is 63 degrees, we can use the sine function to find the height. Here's how:

1. Write down the given information:
- Angle: 63 degrees
- Length of the ladder (hypotenuse): 13 ft

2. Apply the sine function:
sin(63 degrees) = opposite / hypotenuse

3. Rearrange the equation to solve for the opposite side:
opposite = sin(63 degrees) * 13 ft

4. Calculate the height using a scientific calculator or online calculator:
opposite = 0.891 * 13 ft ≈ 11.58 ft

Therefore, the ladder reaches a height of approximately 11.58 feet on the building (rounded to the nearest foot).

h=13Sin63deg