Sine & cosine rules

Lines AB, BC, CD and AD form two triangles.

Work out the length of AD.

Use the sine rule to work out x.

By rounding each number to one significant figure,

You must show your working.

Here is a triangle.

Sam attempts to find the value of cos x using the cosine rule.

Identify two errors Sam has made.

Use the sine rule to work out length x. You must show your working.

x = cm

Here is triangle A.

Use the sine rule to show that x = 64 ° to the nearest degree.

Here is triangle B.

Anna thinks that w must be 64 ° to the nearest degree. She says, “This is because t riangle B has two sides and one angle the same as triangle A.”

Without further calculation, is she correct? Tick a box.

Give a reason for your answer.

Work out the area of triangle ABC.

A boat sails 35 km North from A to B. From B the boat sails to C and then back to A.

Show that the distance the boat sails from C to A is 79 km to the nearest km You must show your working.

Work out the bearing of A from C.

A ship sails from A on a bearing of 247 ° It travels at a constant speed of 23 mph for 1 hours. Is the ship now closer to B than it was when it left A? You must show your working.

ABCDEF is a triangular prism. P is a point on EF.

EB = 29 cm Angle EBP = 35 ° Angle EPB = 114 ° Work out the length of EP.

Use the sine rule to work out the size of angle x.

x = °

Here is a triangle.

Give a reason why the length of side AB cannot be 35 m

Here is a different triangle.

Leah tries to use the sine rule to work out the size of angle x. Here are the first two lines of her working.

What error has she made in this working?

A ship sails from P to Q and then from Q to R. Q is 12 miles from P, on a bearing of 080° R is 28 miles from Q, on a bearing of 155°

Work out the direct distance from P to R.

Work out the value of w.