Question

An observer (O) is located 400 feet from a building (B). The observer notices a kite (K) flying at a 29° angle of elevation from his line of sight. How high is the kite flying over the building? You must show all work and calculations to receive full credit. (10 points)

A right triangle is shown with one leg measuring 400 and another leg measuring h, with an angle across from it measuring 29 degrees.

Answer 1

To find the height of the kite (h) above the building, we can use the tangent function from trigonometry. The setup can be understood as follows:

1. We have a right triangle formed with:
- The horizontal leg (the distance from the observer to the building) measuring 400 feet.
- The vertical leg (the height of the kite above the building) denoted as h feet.
- The angle of elevation from the observer to the kite, which is 29°.

2. The tangent function relates the angle of elevation to the opposite and adjacent sides of the right triangle:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where \(\theta\) is the angle of elevation, the opposite side is h (the height of the kite), and the adjacent side is 400 feet (the distance to the building).

3. Plugging in the values we have:
\[
\tan(29^\circ) = \frac{h}{400}
\]

4. To solve for h, we can rearrange the equation:
\[
h = 400 \cdot \tan(29^\circ)
\]

5. Now, we will compute \(\tan(29^\circ)\). Using a calculator:
\[
\tan(29^\circ) \approx 0.5543
\]

6. Now substituting this back into our equation for h:
\[
h = 400 \cdot 0.5543 \approx 221.72 \text{ feet}
\]

Therefore, the height of the kite flying over the building is approximately **221.72 feet**.