A boy is 20m away from a tree, and he observes that the angle of elevation of a bird on the three is 58°. He is 1.7m tall. How high is the tree?

Answer 1

Let's call the height of the tree "h".

We can create a right triangle with the boy, the tree, and the bird at the top of the tree. The boy's eye level and the top of the tree are the two legs of the triangle, and the line from the boy's eye level to the bird is the hypotenuse.

The boy's eye level to the bird is the height of the tree plus the height of the boy, so the height of the tree plus 1.7 meters is the hypotenuse.

Using trigonometry, we can write the following equation:

tan(58°) = h / 20m

Let's solve for h:

h = 20m * tan(58°)
h ≈ 20m * 1.6017
h ≈ 32.03 meters

Therefore, the tree is approximately 32.03 meters tall.

Answer 2

no, the bird is 32.03 m above his eyes.
So the height of the tree is 32.03 + 1.7 = 33.73 m

Answer 3

Apologies for the oversight. Thank you for pointing that out.

Yes, the height of the tree is 32.03m (height of the bird from the boy's eyes) + 1.7m (height of the boy) = 33.73m.

Therefore, the height of the tree is approximately 33.73 meters.