Question

1. (05.03 mc)

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)

Explanation:

Identify the given values

Using the Angle of Elevation Applications knowledge point

$$
LATEXBLOCK0
$$

Set up the trigonometric equation

Using the Tangent Ratio knowledge point

$$
LATEXBLOCK1
$$

Solve for the height

Using the Tangent Ratio knowledge point

$$
LATEXBLOCK2
$$

Answer:

To find how high the kite is flying over the building, we use the tangent ratio:

$$ \tan(29^\circ) = \frac{h}{400} $$

Solving for \(h\):

$$ h = 400 \cdot \tan(29^\circ) \approx 400 \cdot 0.5543 \approx 221.7\text{ feet} $$

The kite is flying approximately \(221.7\text{ feet}\) over the building.