A man 1.5m tall standing on top of a mountain 293.5m high, observes the angle of depression of two flying boats D and C to be 28 degrees and 34 degrees respectively.

Question

Calculate the distance between two boats. correct to 7 decimal places

Answer 1

flying boats??
I think maybe they are at sea level.
looking from 293.5 + 1.5 = 295 above sea level
from base of mountain (point E) straight up to man is 295 meters
man, E , C is right triangle, 90 deg at E
tan 34 = 295/EC
EC = 295 / tan 34
man, E, D same deal
tan 28 = 295/ED
ED = 295 / tan 28

distance CD = ED - EC

to get 7 decimal places carry more than 7 for ED and EC because you lose precision when you subtract.

Answer 2

By the way my sextant does not work to that accuracy :)

Answer 3

Make your sketch.I let AB be the height of the mountain,A at the top.I also adde the 1.5 m to 293.5 m to get AB = 295 m
In right angled triangle ACB, sin 34=295/AC
AC = 295/sin34

Angle DCA = 146 and angle DAC = 6 degrees
By the sine law,
DC/sin6=AC/sin 28

You do the button pushing

Answer 4

h1 = 1.5 m
h2 = 293.5 m.
h = h1+h2 = 1.5 + 293.5 = 295 m.
Locate point B at foot of mountain.

Tan34 = h/BC = 295/BC.
BC = 437.4 m.

Tan26 = h/BD = 295/BD.
BD = 605 m.

BC + CD = BD.
437.4 + CD = 605,
CD =

Answer 5

Correction: Tan28 = h/BD = 295/BD,
BD = 554.81430728.

BC + CD = BD.
437.4 + CD = 554.8,
CD =