Question

Two ships are sailing on the sea on the two side of the lighthouse. The angle of elevation of the topof the lighthouse is observed from the ships are 30 and 45 respectively. If lighhouse is 100m high, the distance between the two ships

Answer 1

Answer:

The answer will be 273 m

Explanation:

According to the problem from the one ship the angle between the observer and the top of the house is 30 degree and from from the another  ship the angle between the observer and the top of the house is 45 degree.

Let consider a triangle of PQR and the mid point of QR is S

Now  position P is the top of the house

Therefore PS = 100 m

Q and R are the position of the two boats

Therefore,

PS/QS = tan30° = 1/√3 or QS = 100√3 m

similarly, PS/RS = tan45° = 1 or RS = 100 m

Therefore the distance between two boats , QR = (QS+RS) = 100√3+100 = 273 m