A lighthouse is built on the edge of a vertical cliff that is 20 m high above sea-level
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Trigonometry · Applications of Trigonometry
Problem
A lighthouse is built on the edge of a vertical cliff that is 20 m high above sea-level. From a boat at point P on the sea, the angle of depression of the boat from the top of the lighthouse is 30°. After the boat sails 60 m directly towards the cliff to point Q, the angle of depression becomes 45°.
Work out the following:
(a) Calculate the height of the lighthouse (excluding the cliff).
(b) Find the horizontal distance of the boat from the foot of the cliff when it is at point Q.