Trigonometry Question. A helicopter uses a flashlight for searching. The distance from the helicopter to the object is 60m, and the angle of depression of the line of vision from the helicopter to...

Trigonometry Question. 

A helicopter uses a flashlight for searching. The distance from the helicopter to the object is 60m, and the angle of depression of the line of vision from the helicopter to the object is 65 degrees. What is the horizontal distance from the helicopter to the object?

Asked on by paulbarton

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The angle of inclination from the object to the helicopter is the same as the angle of depression from the helicopter to the object.

Draw a right triangle with acute angle `65^@` and hypotenuse length 60. Then the leg adjacent to the acute angle is the horizontal distance from the helicopter to the object, while the leg opposite the acute angle is the vertical height of the helicopter.

Thus the horizontal distance can be found by:

`cos65^@=x/60 ==>x=60cos65^@~~25.4`

The horizontal distance from the helicipter to the object is approximately 25.4m (Exactly `60cos65^@` measured in meters)

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