A 18 -ft ladder leans against a building so that the angle between the ground and the ladder is 82 ^\circ.
How high does the ladder reach on the building?
I don't understand your notation of 82 ^\circ
but I will assume that the ladder makes an angle of 82° with the ground at the foot of the ladder
sin 82° = height/18
height = 18sin82 = appr 17.8 ft
To calculate how high the ladder reaches on the building, we can use trigonometry. The height of the ladder on the building corresponds to the opposite side of the right triangle formed by the ladder, the ground, and the building.
We can use the formula:
sin(angle) = opposite/hypotenuse
In this case, the angle is 82 degrees and the hypotenuse is the length of the ladder, which is 18 feet.
sin(82) = opposite/18
To find the height, we can rearrange the formula:
opposite = sin(82) * 18
Now, we can calculate the height:
opposite = sin(82) * 18
opposite ≈ 17.7 feet
Therefore, the ladder reaches a height of approximately 17.7 feet on the building.
To find out how high the ladder reaches on the building, we can use trigonometry and the concept of right triangles.
In this case, we have a right triangle formed by the ladder, the ground, and the building. The hypotenuse of the right triangle is the ladder, the height of the building is the opposite side, and the distance along the ground is the adjacent side.
In this problem, we are given the angle between the ground and the ladder, which is 82 degrees, and the length of the ladder, which is 18 feet. We want to find the height of the ladder on the building.
To find the height, we can use the sine function, which relates the opposite side of a right triangle to the hypotenuse. The mathematical expression for the sine function is:
sin(angle) = opposite/hypotenuse
Solving for the opposite side, we get:
opposite = sin(angle) * hypotenuse
Substituting the given values, we have:
opposite = sin(82 degrees) * 18 feet
Using a calculator, we find that sin(82 degrees) is approximately 0.9939.
So the height the ladder reaches on the building is:
opposite = 0.9939 * 18 feet
Calculating the height, we get:
opposite ≈ 17.889 feet
Therefore, the ladder reaches approximately 17.889 feet on the building.