Question

Two radar stations A and B, are separated by horizontal distance of (a=500 metres), they both track the position of a plane C by recording angles (alpha), and (beta) at 1 second intervals.

time (sec) 9 10 11
the angle A(alpha) 54.80 54.06 53.34
the angle B (beta) 65.59 64.59 63.62

Note: angles given in degrees

If three successive readings are shown in the table

calculate the speed v of the plane and the climb angle at time t=10 seconds.

the coordinates of the plane can be shown to be as follows,

x =a*(tan(beta))/(tab(beta)- tan(alpha))

y =a*((tan(alpha)*tan(beta))/(tan(beta)-tan(alpha))

here x and y give the normal coordinates
from the first station. we need to find a function in terms of (alpha,Beta)by using calculus then substitute into this
values of alpha,beta when t=10 sec.