Question

An observer (O) spots a bird flying at a 35° angle from a horizontal line to its nest. If the distance from O to B is 21,000 ft, how far is the bird (B) from its nest (N)?

a. 12,045 feet
b. 14,704 feet
c. 16,980 feet
d. 17,202 feet

Answer 1

The question requires using trigonometry to find the distance from the bird to its nest. By applying the cosine function to the given angle and the distance from the observer to the bird, we can solve for the distance, which is approximately 17,202 feet.

Step-by-step explanation:

The question is asking to find the distance from the bird (B) to its nest (N) given an observer (O) spots the bird flying at a 35° angle from a horizontal line to its nest and the distance from O to B is 21,000 ft. We can solve this using trigonometry, specifically the cosine function, which relates the adjacent side of a right-angled triangle (in this case, the distance from the bird to its nest) to the hypotenuse and the angle.

Let's denote the distance from the bird to its nest as 'd'. Using the cosine of the angle, we have:

cos(35°) = adjacent / hypotenuse = d / 21,000 ft

Now, we can solve for 'd' by multiplying both sides by the hypotenuse:

d = cos(35°) × 21,000 ft

After calculating this, we find that the distance 'd' is approximately 17,202 feet, which fits the options given and the correct answer is:

• d. 17,202 feet