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Shape, Space and Measures

Further trigonometry - Higher - Test

To complete this test, you'll need to use some of the following formulas.

The sine rule:

sine rule

or sine rule

The cosine rule:
a2 = b2 + c2 - 2bc cos A
b2 = a2 + c2 - 2ac cos B
c2 = a2 + b2 - 2ab cos C

cosine rule
cosine rule
cosine rule

Area of triangle ABC:
½ ab sin C
or, ½ ac sin B
or, 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.

1.

triangle

Find angle A with the

2.

triangle

Find angle Q with the

3.

triangle

Find the length of YZ with the

4.

Use the sine rule to find angle K (correct to 3 s.f.).

triangle

°

5.

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.).
°

6.

Find the area of triangle ABC (correct to 3 s.f.).

triangle

cm2

7.

Calculate the length of PQ (correct to 3 s.f.).

triangle

cm

8.

Find the length of XZ (correct to 3 s.f.).

triangle

cm

9.

Find the area of triangle PQR (correct to 3 s.f.).

triangle

cm2

10.

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).

triangle

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.).
km

Questions 11 and 12 refer to the cuboid ABCDEFGH.

shape

11.

Calculate the length of EC (correct to 3 s.f.).
cm

12.

What angle does EC make with the base ABCD (correct to 3 s.f.)?
°

Questions 13 and 14 refer to the prism PQRSTU.

shape

13.

Calculate the length of RT (correct to 3 s.f.).
cm

14.

What angle does RT make with the base PQRS (correct to 3 s.f.)?
°

15.

shape

In this diagram of a child's climbing frame, V is directly above B and VB = 2m.

VAB = VCB = 40°

AC = 3m

Calculate the size of ABC

°