Suppose that you are standing at #35# meters from a tree. The angle of elevation to the far side of the tree is #23˚#. From the base of the tree to far side of tree, the angle of elevation is #4˚#. How do you find the height of the tree?

1 Answer
Noah G
Apr 6, 2017

The tree measures approximately #15.35# metres in height.

Explanation:

Create a diagram.

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We have, by angle rules, that the angle opposite the known side length measures #63˚#. Here's how:

Note that a right angle is formed between the ground and the vertical. This means the other angle in this triangle measures #67˚#. Since two angles in two triangles share a common vertex here, we can notice that the angle in the adjacent triangle also measures #67˚#. Since this is also a right triangle, the other angle measures #23˚#. The triangle with the #4˚# angle is also right, so we can say that the angle opposite the known side measures #180˚ - 90˚ - 4 - 23 = 63˚#.

Now, by the Law of Sines, we have:

#(sin63˚)/35 = (sin23˚)/H#, where #H = "height of the tree"#

#H ~~ 15.35 m#

Therefore, the tree has height #15.35# metres.

Hopefully this helps!

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