Sine & cosine rules

Use the cosine rule to show that 3x² +10x − 35 = 0.

Solve the equation

You must use the quadratic formula and show all your working.

Give your answers correct to 2 decimal places.

Evaluate the length of PQ.

You must justify any decision that you make.

The diagram shows a quadrilateral EFGH.

Calculate the area of triangle FGH.

Calculate the size of angle x.

Hence, calculate the total area of the shape.

In the diagram below, AB = 13 cm, AD = 17 cm, BC = 19 cm and DC = 11 cm.

Calculate the size of angle x.

You must show all your working.

Calculate the length of CE.

You must show all your working.

Hence, calculate the area of triangle CGE.

In triangle ABC shown below, AB = 13 cm and BC = 11 cm.

D is a point on AC where BD = 7 cm and DC = 5 cm.

Calculate the size of BAD.

You must show all your working.

The diagram shows a triangle ABC and a circle with centre C. The points B and D lie on the circumference of the circle.

The length of the line AB is 19 cm. The length of the line AC is 29 cm. The radius of the circle is xcm.

Calculate the area of the shaded sector BCD.

Triangle ABC has sides AB = 17 cm, AC = 13 cm and BC = 23 cm, as shown below.

Calculate the size of CAB.

The diagram below shows two triangles ABE and BCD, which are constructed from the straight lines AD and EC crossing at point B.

AE = 11 cm, EB = 13 cm, BC = 10 cm and BD = 7 cm. EAB = 37°.

Diagram not drawn to scale.

Calculate the length CD.

BC is the tangent to the circle at point E, as shown below.

EC = 8 cm, AC = 11 cm and DCE = 31°.

Calculate the length of AE.

Calculate the size of CED.

ABC represents the sector of a circle with radius 7 cm and centre A, as shown below. BAC = x°, AD = 3 cm and BD = 6 cm.

Find the area of the shaded region BCD.

By first calculating the size of BAC, calculate the area of triangle ABC.

You must show all your working.