Question

as as Jackson stands near a helicopter landing pad (on the ground), of the helicopter is 148 m. from the helicopter to where Jackson is standing there is an angle of depression of 42°the direct distance between the helicopter and Jackson is _____ meters.round your answer to the nearest meter.

Answer 1

hello

to solve this question, let's simply draw this scenario to give us a better illustration and approach to this question.

the altitudue distance which is the height or distance of the helicopter to the ground is equal to 148m. x represents the distance (horizontal distance) between Jackson and the helicopter.

we can proceed to use trigonometric ratios to solve this question

SOHCAHTOA

$\begin{gathered} \text{soh}=\sin \theta=\frac{opp}{hyp} \\ \text{cah}=\cos \theta=\frac{adj}{hyp} \\ \text{toa}=\tan \theta=\frac{opp}{adj} \end{gathered}$

here we can use the tangent of the angle to find the horizontal distance (opposite) since we have the value of the angle and height (adjacent)

$\begin{gathered} \tan \theta=\frac{opp}{adj} \\ \theta=42^0 \\ \text{opp}=x \\ \text{adj}=148m \\ \tan 48=\frac{x}{148} \\ \text{cross multiply both sides} \\ x=148\tan 48 \\ x=164.37m \end{gathered}$

from the calculations above, the value of the distance (horizontal) between Jackson and the helicopter is equal to 164.37m