Tricky trigonometry question (distance of a ship) A telescope, that is to be used to view ships out at sea, is placed at the top of a cliff that is **150 m high.** Using suitable diagrams, show how the distance of the ship from the shore could be calculated using the angle at which the telescope is tilted in order to get the ship in its sights. Set out an examplar calculation using a realistic angle of your choice.

Pardon my paint skills but I think you have it like this :

(the triangle is right in O)

Basically you need to compute the distance OB, which can be given by the following formula :

$$\tan(\alpha) = OB/OT$$

Then,

$$OB = tan(\alpha)\cdot OT$$

If you know the angle $\alpha$ you already know the distance OT which is 150m, so you know the distance from the ship to the shore

A "realistic" angle could be 73.3° so the ship is 500m from the shore