Angles of elevation and depression

How to use it

1. 1Draw the vertical and the horizontal ground line first, then place the angle at the ground-level end of the line of sight.
2. 2A depression angle measured at the top transfers unchanged to the elevation angle at the foot, so it never needs converting.
3. 3With the vertical known, $\tan \left(\text{angle}\right)=\frac{\text{height}}{\text{ground distance}}$ gives the distance in one line.
4. 4Two sightings of the same vertical give two ground distances: subtract them when the sightings are from the same side, add them when the observers are on opposite sides.

Step-by-step

1. 1
   $\text{angle of elevation of the cliff top from the boat}=45^{\circ }$

   Why: The two horizontals are parallel, so the depression angle transfers to the boat.

2. 2
   $\tan 45^{\circ }=\frac{30}{d}$

   Why: The cliff is the vertical leg and the required distance is the horizontal leg.

3. 3
   $d=\frac{30}{1}=30\text{m}$