## Exam-Style Question on Trigonometry## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 25. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.

A builder marks out three points A, B and C on the ground such that AB = 11m , AC = 15m and angle BAC = 124^{o}.

(a) Calculate the length of BC.

He next marks a fourth point, D, on the ground at a distance of 12m from B, such that angle BDC is 53^{o}.

(b) Find the size of angle DBC.

(c) Find the area of the quadrilateral ABDC.

The builder digs up and removes the soil under the quadrilateral ABDC to a depth of 90 cm for the foundation of the house.

(d) Find the volume of the soil removed. Give your answer in m^{3}

To transport the soil removed, the builder uses cylindrical drums with a diameter of 46cm and a height of 70cm.

(e) Find the volume of a drum. Give your answer in m^{3}.

(f) Find the minimum number of drums required to transport the soil removed.

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