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