Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Shape and Space 4
18 practice questions
Practice questions
1–3 of 3 · Hard
Question 1
4 marks · Hard
Answer and see the solution →A ship is sailing directly towards a lighthouse. From one point at sea, the angle of elevation from the ship to the top of the lighthouse is 14°. After the ship sails 200 metres closer to the lighthouse in a straight line, the angle of elevation increases to 22°. The height of the lighthouse is h metres.
Calculate the height h of the lighthouse.
Give your answer correct to 3 significant figures.
Question 2
3 marks · Hard
Answer and see the solution →Explain, with reference to the properties of parallelograms and right triangles, how you can use Pythagoras’ theorem to prove that the diagonals of a rhombus are perpendicular.
Write your answer in full sentences.
Question 3
5 marks · Hard
Answer and see the solution →The diagram below shows quadrilateral ABCD with AB = AD = 10 cm, BC = CD = 7 cm, and angle BAD = 120°.
Calculate:
(a)[3 marks]The length of diagonal BD.
(b)[2 marks]The area of quadrilateral ABCD.