Question

Hi please help
Marcus spies a bald eagle in a tall tree. He estimates the height of the tree to be 60 feet and the angle of elevation to the bird from where he stands to be 70°. The leaves on the tree make it difficult for Marcus to watch the bird, so he takes several steps away from the tree to get a better view. He now estimates his angle of elevation to be 52°. How many feet did Marcus step back to gain a better view of the bird? Round your answer to the nearest hundredth of a foot.

Answer 1

Answer:

  25.04 ft

Step-by-step explanation:

You want the distance between points with angles of elevation of 70° and 52° to the top of a 60 ft tree.

Tangent

The tangent relation for a right triangle is ...

  Tan = Opposite/Adjacent

Using this, we can find the distance (d1) from the tree of Marcus's first location:

  tan(70°) = (60 ft)/d1

  d1 = (60 ft)/tan(70°)

Similarly, we can find the distance (d2) from the tree to Marcus's second location:

  d2 = (60 ft)/tan(52°)

Movement

The distance Marcus moved from his first location to his second location was ...

  d2 -d1 = (60 ft)/tan(52°) -(60 ft)/tan(70°) = (60 ft)·(1/tan(52°) -1/tan(70°))

  d2 -d1 ≈ 46.88 ft -21.84 ft = 25.04 ft

Marcus stepped back about 25.04 feet.