Draw a diagram.
Review your basic trig functions
Now it is clear that the distance x between the ships is
x = 30cot23° - 30cot28°
From the top of the mountain 30m. Above the sea level, the angle of depression of two ships lying in a vertical plane with a mountain top measure 28° and 23°. Find the distance between the ships.
2 answers
I made a sketch, showing two right-angled triangles.
One is : base angle 28°, height = 30
tan28 = 30/base
base = 30/tan28
other triangle: let the distance between ships be x
tan23° = 30/(base + x)
base + x = 30/tan23
x = 30/tan23 - base
= 30/tan23 - 30/tan28
= 14.25 m
One is : base angle 28°, height = 30
tan28 = 30/base
base = 30/tan28
other triangle: let the distance between ships be x
tan23° = 30/(base + x)
base + x = 30/tan23
x = 30/tan23 - base
= 30/tan23 - 30/tan28
= 14.25 m