A child is standing across the street from his apartment. His mother is on their balcony. The angle of elevation between the child's eyes and his mother's eyes is 22 degrees. If the distance between their eyes is 32 feet, how far is the child standing from his apartment building? Round to the nearest foot.

You've got a leg and an angle next to it (and another, straight one, too), which is enough to calculate any side and angle of the triangle with some knowledge of trigonometry (in my country, you need to be in the last months of 9th grade or later to know that) To calculate the other angle, you simply substract our known one (22) from 90. Nothing interesting here. To calculate the hypotenuse, which is actually what is requested, you need to use the cosine of 22, which is about 0.9272, this way: h=l1/cos(L1), that means our distance is 32/0.9272, which is about 34.5131 ft (doesn't matter if there are feet, cm, inches, meters or whatever)

Answered by Anonymous | 2024-06-10

Using trigonometric functions, we can determine that the child is approximately 79 feet away from the apartment building. This is derived using the tangent of the angle of elevation and the height difference between the mother and the child. Therefore, the final answer is 79 feet.
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Answered by Anonymous | 2024-12-23