Sine, Cosine & Area Rules (Grade 11) — Worksheet & Memo

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Grade 11 · Trigonometry

Sine, Cosine & Area Rules (Grade 11)

WORKSHEET

Name:

Class:

Date:

Mark

/ 27

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

1
In △ABC, Â = 40°, B̂ = 75° and AC = 12 units. Calculate the length of BC.
(3)
2
In △ABC, AC = 8 units, AB = 5 units and Â = 60°. Calculate the length of BC.
(3)
3
Calculate the area of △ABC if AC = 8 units, AB = 5 units and Â = 60°.
(2)
4
Which rule would you use given three sides and no angles?
(1)
5
Which rule would you use given two angles and one side?
(1)
6
Write down the area rule for △PQR using sides p and q.
(1)
7
In △ABC, a = 7, b = 8, c = 5. Calculate Â to one decimal.
(3)
8
Why can SOHCAHTOA not be used in △ABC above?
(2)
9
Prove that the area of △ABC = ½ab sin C.
(4)
10
Prove the sine rule for △ABC.
(5)
11
What single construction begins the proof of all three rules?
(2)

TOTAL: 27 marks