Math Is Fun Forum

isodel

Member

Registered: 2008-01-04

Posts: 2

Trig

I just CAN'T figure this question out!

From a lookout spot 50 m above sea level on a boat, the captain spots two ships. The angle of depression to the ship due west is 40 degrees. The other ship spotted S 70 w will be seen at an angle of depression of 34 degrees. How far apart are the two ships?

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Trig

The other ship spotted S 70 w will

What do you mean by this?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Trig

"Tangent" means 2 things in math, but one of them is useful here.
The "rise over run" phrase means 50 meters high divided by ("over"  means ÷) the "run".
"Run" is the distance along a flat surface to the boat.
Now tan() on your calculator means height divided by distance along the ground or sea.
(~ means approximately here)
tan(40°)=0.8391~= 50meters ÷ level distance to boat.  Level means stay at one altitude or height.
tan(34°)=0.6745~= 50meters ÷ level distance to south and 70 degrees west of south boat at one level altitude.
ShortDistanceWest=50÷0.8391 -----> 59.59~ meters on a level distance measurement.
LongerDistanceAlmostWest=50÷0.6745 -----> 74.13~ meters on level "running" measurement.
Now the rest of the problem could be
explained better with a little map
of the situation on the flat water.
And get the (x,y) coordinates of
both boats.  Then use distance
formula, which is pythagorean's
theorm to get the distance
between them.
Want more on this?

Last edited by John E. Franklin (2008-01-06 12:56:52)

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