Step-by-step explanation:
the situation establishes 2 triangles :
1 has the corners at the helicopter, then straight down on the water, and then the island.
the other had the corners at the helicopter, then the island, and then from there 100ft straight up in the air.
we have enough information to know all angles, we know one side (100 ft altitude). so, we can use the law of sine to get the other sides (incl. the side representing the distance to the island).
a/sin(A) = b/sin(B) = c/sin(C)
where the angles are always opposite of the corresponding sides.
I personally prefer the first triangle.
the angle between the line of sight helicopter-island and the straight down altitude line is complementary to the angle of depression : 90 - 40 = 50°
then the angle between the straight down altitude line and the ground distance to the island is a right angle (90°).
and the angle between the ground distance and the line of sight is then 180 - 90 - 50 = 40°
(remember, the sum of all angles in a triangle is always 180°)
so,
altitude line / sin(40) = ground distance / sin(50)
ground distance = altitude line × sin(50)/sin(40) =
= 100 × sin(50)/sin(40) = 119.18 ft
