Question

Two helicopters flying at the same altitude are 2000m apart when they spot a life raft below. The raft is directly between the two helicopters. The angle of depression from one helicopter to the raft is 37° and the angle of depression from the other helicopter is 49°. Both helicopters are flying at 170km/h. How long will it take the closer aircraft to reach the raft?

Answer 1

did you make your sketch?
On mine I let the vertical height between the raft and the line of flight be h
and the distance from the 49° helicopter be x km, so the other part is 2 - x km
using the two right-angled triangles,
tan 49° = h/x ---> h = xtan49
tan 37° = h/(2 - x) ----> h = (2-x)tan37

xtan49 = (2-x)tan37
xtan49 = 2tan37 - xtan37
x(tan49 + tan37) = 2tan37

take over

Answer 2

A triangle is formed:
base = 2000 m.,
A = 180 - (37+49) = 94o,
B = 37o,
C = 49o,
Use Law of Sine to solve triangle:
sin94/2000 = sin37/b,
b = 1207 m. = 1.207 km,
sin94/2000 = sin49/c,
c = 1513 m.,

d = V*t,
t = d/V = 1.207/170 = 0.0071h = 25.6 s.