A hunter 1.6 m tall, views a bird on top of a tree at an angle of 45°. if the distance between the hunter and the tree is 10.4 m, find the height of the tree.

  • A 9.0 m
  • B 12. 0 m
  • C 8.8 m
  • D 10.4 m

The correct answer is B. 12. 0 m

Let's find the height of the tree given that a hunter 1.6 m tall views a bird on top of a tree at an angle of 45° and the distance between the hunter and the tree is 10.4 m. We can use trigonometry to solve this problem.

Let h be the height of the tree. Since the hunter is viewing the bird at an angle of 45°, we have \(tan(45°) = \frac{h - 1.6}{10.4}\).

Solving for h, we get \(h = 10.4 tan(45°) + 1.6 = 10.4 + 1.6 = 12\). So, the height of the tree is 12 m.

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