Question

A triangle has sides of length 4, 5, 7 units. Find, to the nearest tenth of a degree, the size of the largest angle.

(Total 4 marks)

2.       O is the centre of the circle which has a radius of 5.4 cm.

          The area of the shaded sector OAB is 21.6 cm2. Find the length of the minor arc AB.

(Total 4 marks)

3.       The circle shown has centre O and radius 6.  is the vector ,  is the vector  and  is the vector .

(a)     Verify that A, B and C lie on the circle.

(3)

(b)     Find the vector .

(2)

(c)     Using an appropriate scalar product, or otherwise, find the cosine of angle .

(3)

(d)     Find the area of triangle ABC, giving your answer in the form a, where a Î .

(4)

(Total 12 marks)

4.       Solve the equation 3 sin2 x = cos2 x, for 0° £ x £ 180°.

(Total 4 marks)

5.       The diagrams show a circular sector of radius 10 cm and angle θ radians which is formed into a cone of slant height 10 cm. The vertical height h of the cone is equal to the radius r of its base. Find the angle θ radians.

(Total 4 marks)

Answer