THE lenth of a run way at an airport is 3 km.two sentries are standing at the starting point and end point respectivly. a helicopter is hovering in a stationary position above the runway. while looking at it the angles of elevation observed by the sentries are 30 degree and 60 degrees respectivly. find the height of the helicopter from the runway
First. draw a picture:
h is the height. From the diagram we have
tan(30°) = h/x ...(1)
tan(60°) = h/(3 - x) ...(2)
We also know that tan(30°) = sqrt(3)/3 and tan(60°) = sqrt(3)
Equations (1) and (2) are two equations in two unknowns (h and x). Can you take it from here?