maths
posted by Ruth on .
A straight highway leads to the foot of a tower of height 50m. From the top of the tower, the angles of depression of two cars standing on the highway are 30 degree and 60 degree. What is the distance between the two cars and how far is each car from the tower ?

The 1st(closest) car:
X1 = Distance from tower.
A1 = 60o = Angle between X1 and hyp.
The 2nd car:
X2 = Dist. bet. the 2 cars.
X1+X2 = Dist. from 2nd car to tower.
A2 = 30o = Angle bet. (X1+X2) and hyp.
tan 60 = 50/X1
X1 = 50/tan 60 = 28.87 m.
tan 30 = 50/(X1+X2)
X1+X2 = 50/tan 30 = 86.60 m.
28.87 + X2 = 86.60
X2 = 57.73 m.