IB · Mathematics: Analysis & Approaches SL & HL · Geometry & trigonometry

Sine & cosine rules: IB Mathematics: Analysis & Approaches questions with answers

Free Sine & cosine rules questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.

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Sine & cosine rules practice questions

Question 1Structured · 7 marksA* challenge

In triangle ABC, BC = 8.4 cm, AC = 10 cm and BÂC = 25°.

(a)

Find the two possible values of AB̂C.

[4]
(b)

Find the difference between the areas of the two possible triangles.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)30.2° or 150°
sin AB̂C10 = sin 25°8.4 (M1)(A1)
30.2° A1
180° − 30.2° = 150° A1
4
(b)30.7 cm2
AĈB = 125° or 5.21° (A1)
12(8.4)(10)sin C for each (M1)
30.7 cm2 A1
3
Question 2Structured · 5 marksA* challenge

In triangle ABC, AB = 10 cm, BC = 8 cm and angle BAC = 35°.

Find the two possible values of angle ACB.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
45.8°, 134°
sine rule (M1)
sin C = 10 sin 35°8 (A1)
45.8° A1
recognizing the ambiguous case (M1)
134° A1
5
Question 3Structured · 7 marks

In triangle ABC, BC = 7 cm, AC = 10 cm and angle ACB = 40°.

(a)

Find AB.

[3]
(b)

Find the area of the triangle.

[2]
(c)

Find angle ABC.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)6.46 cm
cosine rule (M1)
correct substitution (A1)
6.46 cm A1
3
(b)22.5 cm2
½ab sin C (M1)
22.5 cm2 A1
2
(c)84.1°
sine rule (M1)
84.1° A1
2
Question 4Structured · 7 marks

In triangle PQR, PQ = 6 cm, PR = 14 cm and QP̂R = 55°.

(a)

Find QR.

[3]
(b)

Find the area of triangle PQR.

[2]
(c)

Find PQ̂R.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)11.6 cm
QR2 = 62 + 142 − 2(6)(14)cos 55° (M1)(A1)
QR = 11.6 cm A1
3
(b)34.4 cm2
12(6)(14)sin 55° (M1)
34.4 cm2 A1
2
(c)100°
sin PQ̂R14 = sin 55°11.6 (M1)
100° A1
2
Question 5Structured · 8 marksA* challenge

A ship leaves port P and sails 15 km on a bearing of 050° to point A. It then sails 10 km on a bearing of 145° to point B.

(a)

Find the size of angle PÂB.

[2]
(b)

Find the distance PB.

[3]
(c)

Find the bearing of P from B.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)85°
use of parallel north lines (M1)
85° A1
2
(b)17.3 km
PB2 = 152 + 102 − 2(15)(10)cos 85° (M1)(A1)
17.3 km A1
3
(c)265°
sine rule or coordinates to find an angle at B or P (M1)
correct angle (A1)
265.2° A1
3
Question 6Structured · 7 marksA* challenge

In triangle ABC, BC = 8.9 cm, AC = 11 cm and BÂC = 42°.

(a)

Find the two possible values of AB̂C.

[4]
(b)

Find the difference between the areas of the two possible triangles.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)55.8° or 124°
sin AB̂C11 = sin 42°8.9 (M1)(A1)
55.8° A1
180° − 55.8° = 124° A1
4
(b)36.8 cm2
AĈB = 82.2° or 13.8° (A1)
12(8.9)(11)sin C for each (M1)
36.8 cm2 A1
3

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in