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A mapmaker stands 4.5 miles away from the center of a mountain. She uses an instrument called a sextant to site the angle of
elevation to the top of the mountain at 40°. What is the height of the mountain?

Respuesta :

Look at picture for solution.

h = height of mountain

theta = angle of elevation

It can be assumed that the mountain will have its highest point at the center of the mountain.

Ver imagen bm20350
mhanifa

Answer:

  • ≈ 3.8 mi

Step-by-step explanation:

Let the height is h and distance to the center of mountain is d.

Use tangent to find the value of h:

  • tangent = opposite / adjacent
  • tan 40 = h/d
  • h = d tan 40
  • h = 4.5*0.839
  • h = 3.7755 ≈ 3.8 mi

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