Question

Two helicopters, A and B, 25 kilometres apart flying at the same altitude, receive an S.O.S. distress signal from a cap-sized boat (C). The angle of depression from helicopter A to the boat is 40° while the angle of depression from helicopter B to the boat is 30 °.

a) Calculate the distance each helicopter must travel to reach the cap-sized boat.
b) Find the height of the two helicopters
Can someone solve this for me please<33

Answer 1

Did you make a sketch?
If so, then you must have seen that angle C = 110°
You have all the angles plus one side, so the sine law can be used.
AC/sin30 = 25/sin110
AC = 25sin30/sin110 = appr 13.302
find BC in the same way.

Now that we have AC,
sin 40 = h/AC
h = ACsin40 = ...

Answer 2

I'm assuming that
(a) C is between A and B
(b) the choppers plan to fly horizontally to a point just above C.
If that's the case, then if we draw a diagram, and let
x = horizontal distance from A to C
h = altitude of choppers
then we have
h/x = tan30°
h/(25-x) = tan40°
x = 25tan40° / (tan30° + tan40°)

If you want the distance flying directly down to the boat on the water, then use the Pythagorean Theorem once you have h and x.