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Shape, Space and Measures
To complete this test, you'll need to use some of the following formulas.
The sine rule:
The cosine rule:a2 = b2 + c2 - 2bc cos Ab2 = a2 + c2 - 2ac cos Bc2 = a2 + b2 - 2ab cos C
Area of triangle ABC:½ ab sin Cor, ½ ac sin Bor, ½ bc sin A
Where necessary, give answers correct to 3 s.f.
In questions 1-3, state whether you would use the sine rule or the cosine rule to answer the question. Don't find the required side or angle.
Find angle A with the
Find angle Q with the
Find the length of YZ with the
Use the sine rule to find angle K (correct to 3 s.f.).
A triangle has sides of length 5.7cm, 7.1cm and 4.1cm. Use the cosine rule to find the size of the smallest angle (correct to 3 s.f.).
Find the area of triangle ABC (correct to 3 s.f.).
Calculate the length of PQ (correct to 3 s.f.).
Find the length of XZ (correct to 3 s.f.).
Find the area of triangle PQR (correct to 3 s.f.).
A hiker begins her journey at a youth hostel (Y) and walks for 4km on a bearing of 015° to her lunch stop (L). She then walks on a bearing of 110° for 5.2km until she reaches the campsite (C).
This is a sketch of the hiker's journey. Calculate the direct distance from the youth hostel to the campsite (correct to 3 s.f.).
Questions 11 and 12 refer to the cuboid ABCDEFGH.
Calculate the length of EC (correct to 3 s.f.).
What angle does EC make with the base ABCD (correct to 3 s.f.)?
Questions 13 and 14 refer to the prism PQRSTU.
Calculate the length of RT (correct to 3 s.f.).
What angle does RT make with the base PQRS (correct to 3 s.f.)?
In this diagram of a child's climbing frame, V is directly above B and VB = 2m.
= = 40°
AC = 3m
Calculate the size of