Cosine Rule

Calculate the length of YZ, expressing your answer as a surd in its simplest form.

Calculate the length of RS, correct to 3 significant figures.

Calculate the size of angle ACB.

She uses a sharp pencil and carefully rules a line of length 4.8 cm. She then uses her compasses to measure an angle of 37° at one end of the line. Finally, she uses her ruler to draw another line, of length 6.3 cm.

If she has measured her two lengths and the angle accurately, calculate how far apart the ends of her two lines should be
Correct to the nearest millimetre.

Triangle ABC is shown below.

Calculate the length of AB.

A piece of land is in the shape of a triangle as shown.
PQ = 250 m, PR = 180 m, angle QPR = $\displaystyle 147^{\circ}.$
The owner wishes to build a fence along the side QR.

Calculate the length of the fence.

In triangle XYZ:
$\displaystyle XZ=10$ centimetres
$\displaystyle YZ=8$ centimetres
$\displaystyle \cos Z = \frac{1}{8}$

Calculate the length of XY.

Triangle XYZ is shown below.

Calculate the size of the smallest angle in triangle XYZ.

In triangle ABC:
•  AC = 5 metres
•  BC = 6 metres
$\displaystyle \bullet \quad \cos C = \frac{1}{5}$

Calculate the length of AB.

In triangle ABC:
• AB = 25 metres
• AC = 18 metres
• BC = 34 metres.

Calculate the size of the shaded angle at A.