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

Question

A right triangle BNO is shown with angle B marked 35 degrees, side BN marked x, and side BO marked 21,000 feet.

12,045 feet
14,704 feet
16,980 feet
17,202 feet

Answer 1

To find the distance from the bird (B) to its nest (N), we can set up the problem using trigonometric functions in the right triangle BNO, where:

• BO (the distance from the observer O to the bird B) is 21,000 feet.
• The angle ∠B (between the horizontal line and the line from the observer to the bird) is 35°.
• BN (the distance from the bird to the nest) is the side we want to find.

Using the sine function:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]

In this case:

• The opposite side is BN (the distance from the bird to the nest).
• The hypotenuse is BO (the distance from the observer to the bird).

Thus, we can write:

\[ \sin(35°) = \frac{BN}{BO} \]

Substituting the known values, we have:

\[ \sin(35°) = \frac{BN}{21,000} \]

To find BN, we will rearrange the formula:

\[ BN = 21,000 \cdot \sin(35°) \]

Now, calculating \(\sin(35°)\):

\[ \sin(35°) \approx 0.5736 \]

Now substituting this value in:

\[ BN = 21,000 \cdot 0.5736 \approx 12,045.6 \]

Rounding to the nearest whole number, we get:

\[ BN \approx 12,046 \]

Thus, the distance from the bird (B) to its nest (N) is approximately 12,045 feet.

Therefore, the correct answer is:

12,045 feet.