posted by pooi .
Two Trees are 150 m apart. From a point halfway between them, the angle of
elevation of their tops is 15°and..? 15°, and 20°.
a)How much taller is one tree than the other?
b) Where would a person have to stand in order to have the angle of elevation to the top of each tree the same?
I can't believe you drew a diagram and can't see how to solve this.
Anyway, looking at the diagram, let the small tree's height be h, and the tall tree's height be H.
h/75 = tan 15°
h = 20.096
H/75 = tan 20°
H = 27.297
So, at what distance x from the smaller tree do they both have the same angle of elevation? At that point the tangent of both angles will be the same:
20.096/x = 27.297/(150-x)
x = 63.6
So, standing 63.6m from the shorter tree, the tops of both trees will have the same angle of elevation, 17.54°