Hailey is scuba diving in the ocean. her boat is anchored 300 feet away at a 30° angle of depression. if her diving partner is 25 feet directly below her, what is the angle of depression from the boat to hailey's diving partner? (round to nearest whole number)
We first find the height of Halley's position as follows:
Let the height of Hailey's position from the horizonal ground be h, then
tan 30 = h / 300
h = 300 tan 30 = 173.2051 feet.
Thus the height of Hailey's diving partner from the horizontal ground is 173.2051 - 25 = 148.2051
Let the angle of depression from the boat to Hailey's diving partner be x, then
tan x = 148.2051 / 300 = 0.4940
Thus, x = arctan (0.4940) = 26.29
Therefore, the angle of depression from the boat to Hailey's diving partner to the nearest whole number is 26 degrees.
