Question

A helicopter pilot sights a landmark an an angle of depression of 34°. The altitudeof the helicopter is 1,748 feet. To the nearest foot, what is the horizontal distancefrom the helicopter to the landmark?

Answer 1

For the question, we will be making a sketch showing the features in the question.

From the sketch and the question, the angle of depression = 34 degrees

The helicopter height above the ground (altitude) = 1,748 ft

L represents the landmark

x = horizontal distance from the helicopter to the landmark

To solve the question, we need to bring out the right triangle from the sketch

Angle e = 34 degrees (alternate to the angle of depression given)

To get x, we make use of the trigonometrical ratio of tan

`\begin{gathered} \tan \text{ }\theta=(opposite)/(adjacent) \\ \text{From the right triangle, the opposite = 1748} \\ \text{The adjacent = x} \\ \theta=34^0 \\ \tan \text{ 34 =}\frac{\text{1748}}{x} \\ \text{Making x the subject of the formula, we have} \\ x=(1748)/(\tan 34) \\ x=(1748)/(0.6745) \\ x=2591.55 \end{gathered}`

Therefore, the horizontal distance from the helicopter to the landmark to the nearest foot is 2592 feet.