# Exam-Style Question on Trigonometry

## A mathematics exam-style question with a worked solution that can be revealed gradually

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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 = 124o.

(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 53o.

(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 m3

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 m3.

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

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