form a height of 38 meters above sea level, two ships are sighted due west. the angles of depression are 53 degrees and 28 degrees. how far apart are the ships?

d (apart are the ships) = 42.8 meters

Step-by-step explanation:

Given data

h (height) = 38m

Ф₁=53°

Ф₂=28°

d (how far apart are the ships) = ?

Solution

d₅₃° (distance to ship at 53°) = h/tanФ₁

d₅₃°=38/tan (53°)

d₅₃°=28.6m

now

d₂₈° (distance to ship at 28°) = h/tanФ₂

d₂₈°=38/tan (28°)

d₂₈°=71.4m

d (apart are the ships) = d₂₈°-d₅₃°

d (apart are the ships) = 71.4-28.6

d (apart are the ships) = 42.8 meters