math
posted by Dan on .
Alexa and Emma are looking up at their house from the backyard. From alexa's point of view, the top of the house is at an ang;e of elevation of 40 degree. From Emma's point of view, directly closer to the house, it is 60 degree. The house is 15 metres high. How far apart are the two girls?

We draw 2 rt. triangles with a common
ver. side and a shared hor. side with
separate hyp:
X = hor. = X1 + X2 = Alexa's dist. from
the house.
X1 = Emma's dist. from the house.
X2 = The dist. between the girls.
Y = Ver. = 15 m.
tan60 = Y/X1 = 15/X1.
X1 = 15/tan60 = 8.66 m.
tan40 = Y/(X1+X2).
tan40 = 15/(8.66+X2)
8.66+X2 = 15/tan40 = 17.88
X2 = 17.88  8.66 = 9.22 m. = Dist.
between the girls.