Question

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?

Answer 1

The tree measures approximately `15.35` metres in height.

Explanation:

Create a diagram.

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!