Question

Explanations not just answers: Sarah measures the angle of elevation to the top of a tree as 23.6 degrees from the point which is 250 m from its base. Her eye level, where the angle measurement was taken is 1.5 m above the ground. Assuming the ground to be horizontal, find the height of the tree

Answer 1

See the attached diagram.

In the right triangle, x is opposite the 23.6 degree angle, and the adjacent side is 250 m. This suggests using the tangent ratio.


`(x)/(250)=\tan 23.6 ^\circ \\ x=250 \cdot \tan 23.6^\circ \approx 109.2`

Finally, to get the height of the tree, add Sarah's height, 1.5 m.

The tree is approximately 110.7m tall.