# sine and consine rules

• Jan 10th 2011, 07:23 AM
Eftychia
sine and consine rules
A bird leaves a nest, N, and flies 800 m on a bearing of 132 degrees to a tree T. It then leaves T and flies 650 m on a bearing of 209 degrees to a pylon P. Assuming that N, T and P are at the same height above the ground, calculate the distance and bearing on which the bird must fly in order to return directly from P to N.

time: 2h+
• Jan 10th 2011, 07:28 AM
Prove It
Start by drawing the situation and marking in all known sides and angles.
• Jan 10th 2011, 07:32 AM
Eftychia
the calculations are easy?
• Jan 10th 2011, 07:36 AM
snowtea
If you draw the diagram, you will have a triangle with 2 known sides and a known angle in between.

Law of cosines.
• Jan 10th 2011, 07:36 AM
Prove It
Provided you end up with a triangle that has enough known sides/angles in order to solve for the remaining ones, yes.
• Jan 10th 2011, 07:41 AM
Eftychia
ok, thank you guys
• Jan 11th 2011, 11:10 PM
Prove It
Sine Rule:

$\displaystyle \frac{a}{\sin{A}} = \frac{b}{\sin{B}} = \frac{c}{\sin{C}}$ or $\displaystyle \frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}$.

Cosine Rule:

$\displaystyle c^2 = a^2 + b^2 - 2ab\cos{C}$ or $\displaystyle \cos{C} = \frac{a^2 + b^2 - c^2}{2ab}$.