# Angle of depression

• Apr 18th 2007, 08:06 PM
cuteisa89
Angle of depression
Hi,
Can someone help me with this problem?

Find the angle of depression from the top of a light-house 250 feet above water level to the water line of a ship 2 miles offshore.

Thank you so much,
Isabel
• Apr 18th 2007, 08:20 PM
ecMathGeek
Quote:

Originally Posted by cuteisa89
Hi,
Can someone help me with this problem?

Find the angle of depression from the top of a light-house 250 feet above water level to the water line of a ship 2 miles offshore.

Thank you so much,
Isabel

I hope you know how to use the trig functions.

This is a right triangle, where the length of the opposite side is 250ft, the adjacent side is 2miles, and we're looking for the measure of the acute angle.

First, we need to have the units be the same:
A = 250 ft
B = 2 miles = 2*5280 ft = 10560 ft

tan(x) = A/B = 250/10560
x = arctan(250/10560) = 0.023669821 radians = 1.35618085 degrees

• Apr 18th 2007, 08:21 PM
Jhevon
Quote:

Originally Posted by cuteisa89
Hi,
Can someone help me with this problem?

Find the angle of depression from the top of a light-house 250 feet above water level to the water line of a ship 2 miles offshore.

Thank you so much,
Isabel

See the diagram below.

we want the angle x. we know the length of AB and AC, so we can use the tangent ratio to find x.

so tan(x) = 250/10560 = 0.023674242
=> x = arctan(0.023674242)
=> x = 1.356 degrees

EDIT: beaten again! you're too much for me ecMathGeek!
• Apr 18th 2007, 08:25 PM
ecMathGeek
Quote:

Originally Posted by Jhevon
EDIT: beaten again! you're too much for me ecMathGeek!

Well, your diagram is so much better than mine ;).

Always take pride in your work, even when someone has already done it before you. :D
• Apr 18th 2007, 08:39 PM
Jhevon
Quote:

Originally Posted by ecMathGeek
Well, your diagram is so much better than mine ;).

Always take pride in your work, even when someone has already done it before you. :D

easy for you to say, you're the one that came out ahead.

anyway, i guess this is just karma for the few times i did it to Soroban