Question

An observer (0) 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 thebuilding?

Answer 1

GIVEN:

We are given the distance between an observer and a building as 400 feet. Also at an angle of elevation of 29 degrees the observer notices a kite flying above the building.

Required;

To find the distance (h) between the kite and the building.

Step-by-step solution;

From the details provided, we have a right angled triangle labeled KOB. Note that the reference angle is 29 degrees. Therefore the sides are labeled as follows;

$\begin{gathered} Reference\text{ }Angle=29\degree \\ \\ Opposite=KB(h) \\ \\ Adjacent=OB(400) \\ \\ Hypotenuse=KO \end{gathered}$

With the opposite and adjacent sides given, we will now use the following trig ratio;

$tan\theta=\frac{Opposite}{Adjacent}$

We will now substitute the given values into this trig equation;

$tan29\degree=\frac{h}{400}$

Now we cross multiply;

$\begin{gathered} tan29\degree\times400=h \\ \\ 0.554309051453\times400=h \\ \\ 221.723620581=h \end{gathered}$

We can round this to the nearest hundredth and we'll have;

$h\approx221.72ft$

ANSWER:

$h\approx221.72ft$