Non-right-angled triangles: แบบฝึกหัด

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

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.

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

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.

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.

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.