Question

If a plane is descending at an angle of depression of 18° to the nearestairport and are at an altitude of 5,800 feet, how far are they horizontallyfrom the airport? Round to the nearest tenth.

Answer 1

As we have the opposite length of a rigth triangle, the angle and we need to find the adjacent length, we can formulate the following equation with the trigonometric ratio tangent.

`\begin{gathered} \tan (18)=\frac{\text{Opposite length}}{\text{Adjacent length}} \\ \tan (18)=\frac{5800\text{ ft}}{x}\text{ (Replacing the values)} \\ x\cdot tan(18)=5800\text{ ft (Multiplying by x on both sides of the equation)} \\ x=\frac{5800\text{ ft }}{\tan(18)}\text{ (Dividing by tan(18) on both sides of the equation)} \\ x=17850.56\text{ (Dividing)} \\ \text{The answer is 17850.6 ft (Rounding to the nearest tenth)} \end{gathered}`