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

Question id: 665. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is allowed.

Two towers are situated close to each other on level ground. From point C on the ground directly between the two buildings, the angle of elevation to the top of each tower is \( \theta \).

The distance from point C to point A at the top of the taller building is 131 metres.

The distance from point C to point B at the top of the shorter building is 91 metres.

The distance between A and B is 141 metres.

Find the heights of the two towers to the nearest metre.

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