Basic sine rule application

2. In the triangle \(A B C\),

• \(A B = 21 \mathrm {~cm}\)
• \(B C = 13 \mathrm {~cm}\)
• angle \(B A C = 25 ^ { \circ }\)
• angle \(A C B = x ^ { \circ }\)
  1. Use the sine rule to find the value of \(\sin x ^ { \circ }\), giving your answer to 4 decimal places.

Given also that \(A B\) is the longest side of the triangle,

find the value of \(x\), giving your answer to 2 decimal places.

8 In the triangle ABC shown, \(\mathrm { AB } = 8 \mathrm {~cm}\). \(\mathrm { AC } = 12 \mathrm {~cm}\) and angle \(\mathrm { ABC } = 82 ^ { \circ }\). Find \(\theta\) correct to 3 significant figures. \includegraphics[max width=\textwidth, alt={}, center]{1c52d6b5-84b4-455a-9620-c377ae457069-3_382_540_1492_718}

1 The triangle ABC has an obtuse angle at A . The angle at B is \(15 ^ { \circ }\). The length of AC is 10 cm and the length of BC is 13 cm . Calculate the size of the angle at A .

4 The diagram shows a triangle \(A B C\). \(A B\) is the shortest side. The lengths of \(A C\) and \(B C\) are 6.1 cm and 8.7 cm respectively. The size of angle \(A B C\) is \(38 ^ { \circ }\) Find the size of the largest angle.
Give your answer to the nearest degree. \includegraphics[max width=\textwidth, alt={}, center]{ad6590e8-6673-45ca-bef3-a14716978827-05_2488_1716_219_153}

\includegraphics{figure_4} Fig. 4 shows triangle ABC, where AB = 7.2 cm, AC = 5.6 cm and angle BAC = 68°. Calculate the size of angle ACB. [5]

\includegraphics{figure_1} The diagram shows triangle \(ABC\), with \(AC = 13.5\) cm, \(BC = 8.3\) cm and angle \(ABC = 32°\). Find angle \(CAB\). [2]