# Sail Boat Race Trigonometry, just stuck on first part

#### Juntao

I've added a picture thats part of the problem.

A sailboat race course consists of four legs defined by the displacement vectors A, B, C and D shown above.
The values of the angles are È1 = 420, È2 = 410, and È3 = 270.

The magnitudes of the first three vectors are A = 3.7 km, B = 5.3 km and C = 4.8 km. The finish line of the course coincides with the starting line.

The coordinate system for this problem has positive x to the right, positive y as up and counter-clockwise to be a positive angle.

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Now first thing I should do is break up each vector into its components, and then add up all the x and y components to get vector D.

This is what I've tried.

Vector a
x-component = 3.7*cos 42=2.75km
y-component = 3.7*cos42= 2.48km

vector b
x component = 5.3*cos 41=4.00km
y component = 5.3*sin41= 3.48km

vector c
x component = 4.8*cos 27=4.27km
y component= 4.8*sin27= 2.18km
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vctor d
x component = 11.02km
y component = 8.14km

So for vector d, just add up the first 3 components in their respective columns. However, when I calculate D's distance => sqrt(11.02^2+8.14^2), I get the incorrect answer of 13.70km.
So of course, if this answer is wrong, then most likely I figured out one of the components wrong, but I don't know which ones. Please help.

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#### HallsofIvy

Science Advisor
Homework Helper
Did you notice that vector B is going back to the LEFT? Its x component is negative. Both the x component and y component of C will be negative. Also notice that once you have added the components of A, B, and C, the result will be the NEGATIVE of D.

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