Christopher wants to determine how far away a helicopter is from where he is standing. He knows the helicopter is sitting on the edge of a roof of an apartment building that is 400 feet high and 1,050 feet from where he is standing. Using the information in the drawing, approximately how far is the helicopter from Christopher?
Use the Pythagorean Theorem:
400^2 + 1050^2 = d^2
160,000 + 1,102,500 = d^2
1,262,500 = d^2
1,123.6 = d
To determine how far the helicopter is from Christopher, we can use the concept of right triangles and trigonometry.
From the given information, we can identify the following:
1. The height of the apartment building is 400 feet.
2. The horizontal distance between Christopher and the base of the apartment building is 1,050 feet.
We can consider the scenario as a right triangle, with Christopher's position as the right angle. The vertical side of the right triangle represents the height of the building, the horizontal side represents the distance between Christopher and the building, and the hypotenuse represents the distance between Christopher and the helicopter.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse (d) as follows:
d^2 = (400)^2 + (1,050)^2
d^2 = 160,000 + 1,102,500
d^2 = 1,262,500
d ≈ √1,262,500
d ≈ 1,123.92 feet (rounded to the nearest hundredth)
Therefore, the approximate distance between Christopher and the helicopter is approximately 1,123.92 feet.