Q13. - Algebra 2

Question

When landing, a jet will average a $3°$ angle of descent. What is the altitude x, to the nearest foot of a jet on final descent as it passes over an airport beacon 6 miles from the start of the runway?

Step-by-Step Solution

Answer

The value of altitude $x=1660.03 \text{feet}$.

Step 1. Write down the given information.

It is given that on landing the angle of descent of the jet is $3°$. And the runway is 6 miles long.

Step 2. Calculation.

Since, angle of ascent is equal to angle of descent. Therefore, from the given figure $\angle C=3°$ as shown.

Now in right triangle ABC by trigonometric ratios,

 $\begin{array}{c}\tan \left(C\right)=\frac{AB}{BC}\\ \tan \left(3°\right)=\frac{x}{6}\\ x=6\tan \left(3°\right)\\ x=0.3144\text{\hspace{0.33em}miles}\\ x=1660.03\text{\hspace{0.33em}feet }\mathrm{....}\left(\begin{array}{l}\text{Converting miles}\\ \text{ to feet}\end{array}\right)\end{array}$

Since, the value of $x=1660.03 \text{feet}$. Hence, the altitude $x=1660.03 \text{feet}$.

Step 3. Conclusion.

The value of altitude $x=1660.03 \text{feet}$.