Past-Year Questions on Cosine Formula/Rule, Sine Formula/Rule (including ambiguous case)...

Edexcel Past-Year Questions (involving Sine Formula, Cosine Formula, Etc.)

A) Given 2 sides and 1 angle of Δ:

1)        In ΔABC, AB = 7 cm, AC = 6 cm, angle ABC = 42^o and angle ACB = Ө^o.

Find, to 1 decimal place, the 2 possible values of Ө.           (24/3/2004 P1 Q1)

2)        In ΔABC, AB = 5.7 cm, BC = 8.4 cm, angle ACB = 42^o.

Find, to the nearest 0.1^o, the 2 possible sizes of angle BAC.  (15/01/2010 P1 Q1)

3)    In triangle ABC, AB = 4.6 cm, AC = 5.7 cm and angle C = 52^o. Angle B is acute.

Calculate, to the nearest 0.1^o, the size of angle B.   (14/01/2011 P1 Q2)

4)    In ΔABC, BC = 12 cm, AC = 10 cm, angle ACB = 48^o.

Find, to 3 significant figures,

(a)    the length of AB,

(b)   the size of angle BAC                                      (27/05/2004 P1 Q3)

5)        In ΔLMN, LM = 5.6 cm, LN = 8.2 cm, angle MLN = 57^o.

Find, to 3 significant figures,

a)      the length of MN,

b)      the size of angle LMN                                      (17/05/2007 P2 Q3)

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B) Given 2 angles and 1 side of Δ:

6)        In ΔABC, angle A = 45^o and B = 60^o and AB = 7 cm.

Calculate to 3 significant figures, the length of BC.   (26/05/2006 P2 Q1)

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C) Given 3 sides of Δ

7)        A triangle has sides of lengths 4.6 cm, 5.3 cm and 6.5 cm.

Find, to the nearest degree, the size of the largest angle of the triangle.

                                                                                         (23/01/2007 P2 Q1)

8)        Triangle LMN has LM = 5 cm, LN = 8.2 cm and MN = 6.4 cm

Calculate, in degrees to the nearest 0.1^o, the size of angle LMN.

                                                                                         (21/01/2008 P1 Q1)

9)        The lengths of the sides of a triangle are 4 cm, 5 cm and 6 cm.

Find, in degrees to 1 decimal place, the size of the largest angle of the Δ.

                                                                                         (12/05/2008 P1 Q1)

10)    The lengths of the sides of a triangle are 5 cm, 6 cm and 8 cm.

(a)    Find, in degrees to 1 decimal place, the size of the smallest angle of the Δ.

(b)   Find, to the nearest cm², the area of the Δ.                   (13/05/2010 P1 Q4)

11)    In ΔABC, AB = 5 cm, BC = 8.3 cm and AC = 6.9 cm

(            a)    Find, in degrees to the nearest 0.1^o, the size of angle ACB.

(            b)   Find, in cm², to 3 significant figures, the area of ΔABC.

(18/01/2010 P2 Q2)

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Q12 to Q14 have to be scanned and shown below because the blogging software cannot produce the drawn triangles as they are - perhaps certain plug-in needed:

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