20. You have climbed to the top of a tall tree. When you get to the top, you use your clinometer to discover that the angle between the tree and the line of sight to your red lunchbox is 30o. You know you left the lunchbox 20 meters from the base of the tree. How tall is the tree? (Careful! This is a little different than the building problems!)
A 75.36 m
B 92.09 m
C 20.17 m
D 51.25 m
E 18.95 m
F 34.64 m
I am not sure whether the angle 30 is perhaps supposed to be the angle made with the vertical line of the tree and the line towards
the ground to the lunchbox . If this understanding is correct then you could work out the other angle using the fact that the
3 angles of a triangle add up to 180 meaning that if one is 90 then first do 180-90 to get the sum of the other two then
30 + 60 = 90
On this basis perhaps it is trying to lead to 20*Tan(60).
Notice you can get the same result by using h as the adjacent (with TAN) and 20 as opposite.
Tan (30) = opposite/adjacent
Tan (30) = 20 / h
h = 20 / (Tan(30)) = ...
Or with 60 degrees make sure that the "opposite" is indeed opposite the angle and do it that way.
It did wonder whether the hypotenuse was going to be 20 (direct line, rather than horizontal), but it does say the base of the
tree, and this would not fit any of the options anyway so that cannot be the case.
It might be a good idea to draw a diagram getting the measurements according to an approximate scale if you are not sure.
My first answer is one of the options, and I suppose if it is a tall tree the angle of 60 degrees from horizontal would be more likely.