Respuesta :

Answer:

The height of the hill is 131ft

See explanation in the photo

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mhanifa

Answer:

  • 91 feet

Step-by-step explanation:

Refer to attached picture

Let the base is b and the height of the hill is x.

For the smaller triangle we have:

  • x/b = tan 39.3°

And for the bigger triangle:

  • (x + 40)/b = tan 49.7°

Solve both equations for b:

  • b = x/ tan 39.3°
  • b = (x + 40)/tan 49.7°

Eliminate b and get the values of tan, solve for x:

  • x/ tan 39.3° = (x + 40) / tan 49.7°
  • x tan 49.7° = (x + 40) tan 39.3°
  • x( 1.179) = x(0.819) + 40(0.819)
  • x(1.179 - 0.819) = 32.76
  • x = 32.76/0.36
  • x = 91 feet (rounded to the nearest foot)
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