A man 1.5m tall, standing on top of a mountain 298.5m high, observes the angles of depression of two flying boats D and C to be 28 degrees and 34 degrees respectively. Calculate the distance between the boats, correct to 1 decimal place.

Answer 1

Hint:
My sketch has two right-angled triangles with the same height
Think parallel lines and "transversals"
Can you find the bases of these two triangles?

Answer 2

Locate point A at base of mountain,
Tan34 = (h1+h2)/AC = (298.5+1.5)/AC,
AC*Tan34 = 300,
AC = 445 m. = Distance of boat C from base of mountain.

Tan28 = 300/AD,
AD = 564 m. = Distance of boat D from base of mountain.

AC + CD = AD,
445 + CD = 564,
CD = Distance between the boats.