Cambridge IGCSE · Mathematics (0580)

Non-right-angled triangles: Practice Questions

2 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Non-right-angled triangles.

6 questions23 marksFree, no account

Question 1

1 mark

In triangle \(ABC\), side \(AB = 5\) cm and side \(AC = 8\) cm. The angle \(\angle BAC = 60^{\circ}\).
Find the length of the side \(BC\).

Question 2

1 mark

In triangle \(PQR\), side \(PQ = 8\) cm, side \(QR = 11\) cm and the included angle \(\angle PQR = 150^{\circ}\).
Calculate the area of the triangle.

Question 3

4 marks

In triangle \(ABC\), the side \(AB = 5\) cm, \(BC = 8\) cm, and the angle \(\angle ABC = 60^{\circ}\). Calculate the length of the side \(AC\).

Write your answer out first, then check it against the worked solution.

Question 4

5 marks

In triangle \( XYZ \), the lengths of the sides are \( XY = 6 \) cm, \( YZ = 10 \) cm, and \( XZ = 14 \) cm. Find the size of the largest angle in the triangle.

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Question 5

5 marks

In triangle \(XYZ\), the length of \(XY = 7\) cm, \(YZ = 10\) cm and the angle \(\angle XYZ = 60^\circ\).

(a) Calculate the length of the side \(XZ\). Give your answer correct to 2 decimal places.

(b) Calculate the area of triangle \(XYZ\), giving your answer in exact form.

Write your answer out first, then check it against the worked solution.

Question 6

7 marks

In triangle \( ABC \), the side length \( AB = 8 \) cm, \( BC = 11 \) cm, and angle \( ABC = 110^\circ \).

(a) Calculate the length of side \( AC \), giving your answer correct to 2 decimal places.
(b) Calculate the area of triangle \( ABC \), giving your answer correct to 1 decimal place.
(c) Find the size of the smallest angle in triangle \( ABC \), giving your answer correct to 1 decimal place.

Write your answer out first, then check it against the worked solution.

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