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)

Question

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.