A roofer is standing on the roof of a house 60 ft above the ground. His truck is parked 25 ft from the house.
What is the angle of depression from the roofer to his truck?
Round to the nearest whole degree.
22°
23°
67°
68° <my answer choice
tan Ø = 60/25 = 2.4
Ø = tan^-1 (2.4) = 67.38..°
= 67° to the nearest degree
To find the angle of depression from the roofer to his truck, we can use trigonometry. The angle of depression is the angle formed between the line of sight from the roofer to his truck and the horizontal ground.
In this case, the height difference between the roofer and the ground is 60 ft, and the horizontal distance between the roofer and the truck is 25 ft.
The tangent function can be used to calculate the angle of depression, which is given by:
tan(angle) = opposite / adjacent
In this scenario, the opposite is the height difference (60 ft) and the adjacent is the horizontal distance (25 ft).
tan(angle) = 60 / 25
Using a calculator:
angle ≈ arctan(60/25) ≈ 67.38°
Rounding this to the nearest whole degree, we get approximately 67°.
Therefore, the correct answer is 67°.
To find the angle of depression from the roofer to his truck, we can use trigonometry. In this case, we can use the tangent function.
The angle of depression is defined as the angle between the line of sight from the roofer to his truck and a horizontal line. In other words, it is the angle formed between the ground and the line connecting the roofer and the truck.
First, let's draw a right triangle to represent the situation. The height of the roofer above the ground is 60 ft, and the horizontal distance from the roofer to the truck is 25 ft. The line connecting the roofer and the truck will be the hypotenuse of the right triangle.
Now, we can use the tangent function (tan) to find the angle of depression.
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the roofer (60 ft) and the adjacent side is the horizontal distance to the truck (25 ft).
tan(angle) = 60/25
To find the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(60/25)
Calculating this answer gives us approximately 67.38 degrees.
Since we are asked to round to the nearest whole degree, the angle of depression from the roofer to his truck is approximately 67 degrees. Therefore, the closest answer choice is 67°.