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

Question id: 107. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.

The Tamarack triathlon race consists of swimming, cycling and running. Competitors swim from A to B, then cycle from B to C and finally run from C back to A.

Angle ACB is 22^{o}.

It takes Walter 10 minutes and 20 seconds to cycle from B to C at a speed of 29kmh^{-1}.

(a) Find the distance from B to C in kilometres.

The distance from C to A is 4 kilometres. Running this part of the course takes Walter 25 minutes.

(b) Calculate the speed, in kilometres per hour, that Walter runs from C to A.

(c) Calculate the distance, in kilometres, from A to B.

(d) Calculate the total distance, in kilometres, of the triathlon course.

(e) Find the size of angle ABC.

(f) Calculate the area of the triathlon course bounded by the lines AB, BC and CA.

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