Pearson Edexcel IGCSE · Mathematics (Specification B)
2 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Trigonometry.
A ship sails from point \(A\) on a bearing of \(060^{\circ}\) for \(15\) km to point \(B\). From point \(B\), the ship changes course and sails on a bearing of \(150^{\circ}\) for \(20\) km to reach point \(C\). Calculate the direct distance between point \(A\) and point \(C\).
In triangle \(ABC\), the length of side \(AB = 7\) cm, the length of side \(BC = 10\) cm, and the size of angle \(B = 150^{\circ}\). Calculate the area of the triangle.
A vertical flagpole stands on horizontal ground. From a point 15 m from the base of the flagpole, the angle of elevation of the top of the flagpole is \(28^\circ\).
Calculate the height of the flagpole, in meters, to 3 significant figures.
Write your answer out first, then check it against the worked solution.
In triangle \(PQR\), \(PQ = 5\) cm, \(PR = 8\) cm, and angle \(QPR = 60^\circ\). Calculate the length of \(QR\).
Write your answer out first, then check it against the worked solution.
In triangle \(ABC\), \(AB = 10\) cm, \(BC = 6\) cm, and angle \(BAC = 30^\circ\). Find the size of the obtuse angle \(ACB\), giving your answer to 1 decimal place.
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In triangle \(ABC\), the length of side \(AB = 8\) cm, the length of side \(BC = 11\) cm and angle \(ABC = 120^\circ\).
(a) Calculate the length of \(AC\), giving your answer in cm to 3 significant figures.
(b) Calculate the area of triangle \(ABC\), giving your answer in cm\(^2\) to 1 decimal place.
(c) Point \(D\) lies on the line segment \(AC\) such that \(BD\) is perpendicular to \(AC\). Calculate the length of \(BD\), giving your answer in cm to 2 decimal places.
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A surveyor stands at point \(P\) and observes two towers, \(A\) and \(B\). Tower \(A\) is on a bearing of \(035^\circ\) from \(P\) and is 450 m away. Tower \(B\) is on a bearing of \(125^\circ\) from \(P\) and is 600 m away.
(a) Calculate the distance between Tower \(A\) and Tower \(B\).
(b) Calculate the bearing of Tower \(B\) from Tower \(A\), giving your answer to the nearest degree.
Write your answer out first, then check it against the worked solution.
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