Question

An observer (o) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. If the distance from the observer (o) to the bird (b) is 15,000 feet, how far is the bird (b) from its nest (n)? Round to the nearest whole number.

a. 8,604 feet
b. 12,287 feet
c. 18,366 feet
d. 21,422 feet

Answer 1

To find the distance from the bird to its nest, we use the cosine of the angle of elevation (55°) and multiply it by the distance from the observer to the bird (15,000 feet). After rounding, the distance from the bird to its nest is approximately 8,604 feet.

Step-by-step explanation:

To determine how far the bird (b) is from its nest (n), we can use trigonometric ratios. Since we have the angle of elevation from the horizontal at the observer's position, and the distance from the observer to the bird, we can create a right triangle. The distance from the observer to the bird is the hypotenuse, and we are trying to find the adjacent side which is the distance from the bird to its nest (let's call this x).

Using the cosine of the angle:

1. Calculate the cosine of 55°: ℓ(cos(55°)).
2. Multiply the cosine of 55° by the hypotenuse (15,000 feet) to find x: ℓ(cos(55°)) × 15,000 feet = x.
3. Round the result to the nearest whole number to get the answer.

Performing the calculation: cos(55°) is approximately 0.5736 (rounded to 4 decimal places), and 0.5736 × 15,000 feet is approximately 8,604 feet when rounded to the nearest whole number.

Therefore, the correct answer is 8,604 feet, which corresponds to option a.