Question

From the top of $20$ metres high lighthouse, the angle of depression of the ship of ${30^ \circ }$ . Find the distance between the ship and the lighthouse.

Answer 1

Hint : As we know that the above given question is a word problem. A problem is a mathematical question written as one sentence or more describing a real life scenario where that problem needs to be solved by the way of mathematical calculation. We can solve the given problem by applying the method of trigonometric values.

Complete step-by-step answer :
We need to first understand the requirement of the question which is distance. We will first draw a diagram according to the question.

Here in the diagram $AB$ is $20\;m$ and $AC = x$ .
Now $\angle DBC = \angle ACB = {30^ \circ }$ .
Let $AB$ is a $20m$ high lighthouse and a ship is at the point $C$ .
Now in the triangle $\tan {30^ \circ } = \dfrac{{AB}}{{AC}}$ .
We know that the value of $\tan 30 = \dfrac{1}{{\sqrt 3 }}$ ,
by substituting the value we get;
$\dfrac{1}{{\sqrt 3 }} = \dfrac{{20}}{x}$ .
On further simplifying we get,
$x = 20\sqrt 3 m$ .
Hence the distance between the ship and the light house is $20\sqrt 3 m$ .
So, the correct answer is “ $20\sqrt 3 m$ ”.

Note : We should always be careful what the question is asking. We should also remember the trigonometric values before solving this kind of question. Based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation or by unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.