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The pilot of a glider plane wants to estimate his altitude. He picks a landmark ahead and measures the angle of depression to be 20 degrees. He flies another 800 feet towards the landmark, remaining at the same altitude. The angle of depression from his new location to the same landmark is now 21.4 degrees. What is the glider's altitude?

Respuesta :

Edufirst

Answer:

  • 4,000 ft

Explanation:

The figure attached shows sketches the situation described.

You have two right triangles.

For the right triangle with the plane on the position A, you can write:

  • tan(20º) = H/(800 + x)

         ⇒ H = (800 + x) tan(20º)

For the right triangle with the plane on the position B, you can write:

  • tan(21.4º) = H/x

        ⇒ H = x tan(21.4º)

To solve, equal both equations:

  • x tan(21.4º) = (800 + x) tan(20º)

  • x tan(21.4º) = 800 tan(20º) + x tan(20º)

  • x = 800 tan(20º) / ( tan(21.4º) - tan(20º) )

  • x = 10,426.9 feet

Substitute in the equation H = x tan(21.4º)

  • H = 10,426.899856 × tan(21.4º) = 4,086 ft

Rounding to one signficant figure that is 4,000 ft.

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