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From a hot-air balloon, Madison measures a 36 angle of depression to a landmark that’s 785 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

Respuesta :

ajeigbeibraheem

The vertical distance above the ground is 570.34 ft

What is an angle of depression?

The angle of depression refers to the angle formed by the horizontal and a downward angle to an object. The line of sight of an observer is usually positioned below the horizontal.

From the given information;

  • the angle of depression is measured as 36°
  • the horizontal distance = 785 feet

To determine the vertical distance above the ground, we need to use the tangential trigonometric ratio. i.e.

[tex]\mathbf{tan \ \theta = \dfrac{opp}{adj}}[/tex]

[tex]\mathbf{tan \ 36 = \dfrac{h}{785 \ ft}}[/tex]

h = 785 tan 36°

h = 570.335 ft

h = 570.34 ft (to the nearest tenth foot)

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