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

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Grade 11 · Trigonometry

Sine, Cosine & Area Rules (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
In △ABC, Â = 40°, B̂ = 75° and AC = 12 units. Calculate the length of BC.
(2)
BCsin40° = 12sin75° → BC = 7,99 units✓✓ (2)
2
In △ABC, AC = 8 units, AB = 5 units and Â = 60°. Calculate the length of BC.
(2)
BC² = 64 + 25 − 80cos60° = 49 → BC = 7 units✓✓ (2)
3
Calculate the area of △ABC if AC = 8 units, AB = 5 units and Â = 60°.
(2)
12(8)(5)sin60° = 17,32 square units✓✓ (2)
4
Which rule would you use given three sides and no angles?
(2)
The cosine rule, rearranged as cos A = b² + c² − a²2bc✓✓ (2)
5
Which rule would you use given two angles and one side?
(2)
The sine rule✓✓ (2)
6
Write down the area rule for △PQR using sides p and q.
(2)
Area = 12·pq·sin R✓✓ (2)
7
In △ABC, a = 7, b = 8, c = 5. Calculate Â to one decimal.
(2)
cos A = 64 + 25 − 492(8)(5) = 4080 = 0,5 → Â = 60,0°✓✓ (2)
8
Why can SOHCAHTOA not be used in △ABC above?
(2)
It is not right-angled — SOHCAHTOA is only defined for right-angled triangles.✓✓ (2)

TOTAL: 16 marks