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abd12 · Dec 12, 2010, 07:50 PM

A boat travels 6km on a true bearing of 120 degrees and
Then 4km on a true bearing of 080 degrees.

a) How far east is the boat from the starting point on the completion of its journey?
b) How far south is the boat from the starting point on the completion of its journey?
c) What is the bearing of the boat from the starting point on the completion of its journey?

Unknown008 · Dec 13, 2010, 02:59 AM

Show your work first.

To help you solve this, it is strongly advised that you make a sketch.

abd12 · Dec 13, 2010, 04:01 AM

The answers, that back of the book are a) 9.135km b). 2.305km c) 104 degrees and 10 minutes bearing.
I tried sketching bearing triangle or some sort of bearing, but I got for section a is 9.196km,
Please correct me, if I am wrong :(.

Unknown008 · Dec 13, 2010, 04:10 AM

For a), you have to divide the triangle into two right angled triangles.

The horizontal side of the first triangle can be found using the cos ratio.

$\cos(30) = \frac{x_1}{6}$

The horizontal side of the second triangle can by found using the sin ratio.

$\sin(80) = \frac{x_2}{4}$

Add those two together and you'll get: 9.135 km

Can you try the next parts?

Part b can be solved using the same process, but with sin and cos ratios respectively instead of the ratios I just used.

Part c is obtained taking the answers to a and b together to make a big triangle and the tan ratio.