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Trigonometry · Guided Practice

Sine Rule

10 questions with answers and video solutions. Try each one before revealing the answer.

1
In triangle ABC, AC = 26 mm, angle B = 114° and angle C = 32°.

Triangle ABC with side AC, angle B, and angle C

Calculate the length of AB in millimetres, correct to 3 significant figures.

2
In triangle PQR, PR = 16 cm, sin Q = 0.8 and sin R = 0.7.

Triangle PQR with side PR, sin Q, and sin R

Calculate the length of PQ.

3
A triangle ABC is such that AB = 6 cm, angle A = 12° and BC = 2.5 cm.
Find the two possible values of angle C.
4
Frank and Sean are standing 54 metres apart on a horizontal football pitch. Frank is at F and Sean is at S. They are each looking at a stationary drone D in the air above the pitch.

Diagram of Frank, Sean, and a drone

The angle of inclination of D from F is 38°.
The angle of inclination of D from S is 49°.

Calculate the height of the drone above the ground, correct to 3 significant figures.

5
2014 P1 Q5
3 Marks

In triangle KLM
•  KM = 18 centimetres
•  sin K = 0·4
•  sin L = 0·9

Triangle KLM with side KM, sin K, and sin L

Calculate the length of LM.

6
2018 P2 Q9
3 Marks

In this diagram:
•  angle ABD = 75∘\displaystyle 75^{\circ}
•  angle BDC = 37∘\displaystyle 37^{\circ}
•  BC = 20 centimetres.

Triangle diagram

Calculate the length of DC.

7
2019 P2 Q19
5 Marks

Katy and Mona are looking up at a hot-air balloon.
In the diagram below, K, M and B represent the positions of Katy, Mona and the balloon respectively.

Triangulation diagram for hot air balloon

•  The angle of elevation of the balloon from Katy is 52°
•  The angle of elevation of the balloon from Mona is 34°
•  Katy and Mona are 350 metres apart on level ground
Calculate the height of the hot-air balloon above the ground.

8
2021 P2 Q4

In triangle PQR
•  PR = 11.3 metres
•  QR = 9.8 metres
•  angle QPR = 54°

Triangle PQR with side lengths and angle

Calculate the size of acute angle PQR.

9
2023 P2 Q4
3 Marks

The diagram shows triangle JKL.
•  Angle KJL = 25°
•  JL = 10 metres
•  KL = 7 metres

Triangle JKL with side lengths and angle

Calculate the size of acute angle JKL.

10
2024 P2 Q13
5 Marks

In triangle ABC:

Triangle ABC with altitude BD

• AC = 22 centimetres
• angle BAC = 40°
• angle BCA = 30°
• BD is perpendicular to AC.
Calculate the length of BD.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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