IB Geometry and Trigonometry Problem 007

At the foot of a hill stands a vertical tower \(TA\) of height \(36\,m\). A straight path climbs the hill from \(A\) to a point \(U\). This information is shown in the following figure.

The figure is not to scale.

image essential to understanding the question

The path makes an angle of \(4^\circ\) with the horizontal.

Point \(U\) on the path is \(25\,m\) from the base of the tower.

The top of the tower is connected to \(U\) by a cable of length \(x\) (in \(m\)).

  1. Complete the figure by clearly showing the information above.
  2. Find \(x\).
Published by Annie Bernatchez in «Geometry and Trigonometry». Key Words: IB, question