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As Jackson stands near a helicopter landing pad (on the ground), he sees a helicopter approaching. The altitude (height above the ground) of the helicopter is 148 meters. From the helicopter to where Jackson is standing there is an angle of depression of LaTeX: 42^\circ42 ∘.


The direct distance between the helicopter and Jackson is _______ meters.


Round your answer to the nearest meter. Type in only the numerical part of the answer (no units).

Sagot :

ajdonis

Answer:

D=221 m

Step-by-step explanation:

In order to solve this problem, we can start by drawing a diagram of the given situation. (see attached picture)

As you may see, we have a right triangle there, so we can use trigonometric functions to solve this. Specifically, the sine function.

[tex]sin \theta = \frac{OS}{Hyp}[/tex]

in this case we need to find the hypotenuse, so we solve the equation above for the Hyp, so we get:

[tex]Hyp= \frac{OS}{sin \theta}[/tex]

in this case, the opposite side (OS) is the heght of the helicopter, the angle is the 42° and the Hyp is the direct distance between the helicopter and Jackson, so we substitute the given data to get:

[tex]Distance=\frac{148m}{sin 42^{o}}[/tex]

Which yields:

D=221m

View image ajdonis
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