A vertical post TF stands on level ground. The angle of depression from T to B is 25 degrees and from T to A is 18 degrees. B and A are on the ground such that F, B, A are collinear and B is between F

here are the solutions to the questions:

17. a) Let T be the top of the post and F be the foot of the post. Let H be the height of the post. Points A and B are on the ground, on the same line as the foot of the post. Point B is nearer to the foot of the post (F) than point A. The angle of depression from T to B is $25^\circ$. The angle of depression from T to A is $18^\circ$. The distance between A and B is $70 \text{ m}$.

Here is a sketch representing the positions:

      T (Top of post)
      | \
      |   \
      |     \
      |       \
      |         \
    H |           \
      |             \
      |               \
      |                 \
      F-------------------B-------------------A
      <---- x ----><----- 70m ----->

In the sketch:

• TF is the height of the post, H.
• F is the foot of the post.
• B is a point on the ground, closer to F.
• A is a point on the ground, further from F.
• $\angle TBF = 25^\circ$ (angle of elevation from B to T, which is equal to the angle of depression from T to B).
• $\angle TAF = 18^\circ$ (angle of elevation from A to T, which is equal to the angle of depression from T to A).
• Distance FB = $x$.
• Distance AB = $70 \text{ m}$.
• Distance FA = $x + 70 \text{ m}$.