IB · Mathematics: Applications & Interpretation SL & HL · Geometry & trigonometry

Trigonometry & bearings: IB Mathematics: Applications & Interpretation questions with answers

Free Trigonometry & bearings questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.

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Trigonometry & bearings practice questions

Question 1Structured · 7 marksA* challenge

Two boats leave harbour H at the same time. Boat P sails 15 km on a bearing of 065°. Boat Q sails 10 km on a bearing of 165°.

(a)

Write down the size of angle PHQ.

[1]
(b)

Find the distance PQ.

[3]
(c)

Find the bearing of Q from P.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)100°
100° A1
1
(b)19.4 km
cosine rule (M1)
PQ2 = 152 + 102 − 2(15)(10)cos 100° (A1)
19.4 km A1
3
(c)215°
angle HPQ = 30.5° (sine rule) (M1)(A1)
bearing 215° A1
3
Question 2Structured · 6 marks

From a point A on level ground, the angle of elevation of the top T of a vertical tower is 28°. From a point B, 60 m closer to the tower, the angle of elevation is 50°.

(a)

Find the size of angle ATB.

[1]
(b)

Find the length BT.

[3]
(c)

Find the height of the tower.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)22°
50° − 28° = 22° A1
1
(b)75.2 m
BTsin 28° = 60sin 22° (M1)(A1)
75.2 m A1
3
(c)57.6 m
BT sin 50° (M1)
57.6 m A1
2
Question 3Structured · 5 marks

A ship sails 12 km on a bearing of 060° and then 8 km on a bearing of 170°.

(a)

Find the distance of the ship from its starting point.

[3]
(b)

Find the bearing of the ship from its starting point.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)11.9 km
angle between legs (A1)
cosine rule (M1)
11.9 km A1
3
(b)99.1°
sine rule or coordinates (M1)
99.1° A1
2
Question 4Structured · 7 marksA* challenge

Two boats leave harbour H at the same time. Boat P sails 18 km on a bearing of 040°. Boat Q sails 14 km on a bearing of 140°.

(a)

Write down the size of angle PHQ.

[1]
(b)

Find the distance PQ.

[3]
(c)

Find the bearing of Q from P.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)100°
100° A1
1
(b)24.6 km
cosine rule (M1)
PQ2 = 182 + 142 − 2(18)(14)cos 100° (A1)
24.6 km A1
3
(c)186°
angle HPQ = 34.0° (sine rule) (M1)(A1)
bearing 186° A1
3
Question 5Structured · 6 marks

From a point A on level ground, the angle of elevation of the top T of a vertical tower is 24°. From a point B, 40 m closer to the tower, the angle of elevation is 42°.

(a)

Find the size of angle ATB.

[1]
(b)

Find the length BT.

[3]
(c)

Find the height of the tower.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)18°
42° − 24° = 18° A1
1
(b)52.6 m
BTsin 24° = 40sin 18° (M1)(A1)
52.6 m A1
3
(c)35.2 m
BT sin 42° (M1)
35.2 m A1
2
Question 6Structured · 5 marks

A ship sails 20 km on a bearing of 075° and then 10 km on a bearing of 185°.

(a)

Find the distance of the ship from its starting point.

[3]
(b)

Find the bearing of the ship from its starting point.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)19.1 km
angle between legs (A1)
cosine rule (M1)
19.1 km A1
3
(b)105°
sine rule or coordinates (M1)
105° A1
2

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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