Trigonometry：练习题

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.

In triangle \(PQR\), \(PQ = 5\) cm, \(PR = 8\) cm, and angle \(QPR = 60^\circ\). Calculate the length of \(QR\).

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.

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.

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.