Question

A light-house $100$ m high observe that two ships are approaching it from West and South respectively. If the angles of depression of the two ships are $30$ ${}^{\circ }$ and $45$ ${}^{\circ }$ respectively, then the distance between the two ships is -

• A. $100(\sqrt{3}+1)$ m
• B. $100(\sqrt{3}+1{)}^2$ m
• C. $200$ m
• D. $400$ m

Answer 1

Answer: (C)

$200$ m

we can observe that in $△ABC$

$\tan {45}^o=\frac{100}{a}\Rightarrow a=100$

Similarly, in $△ACD$

$\tan {30}^o=\frac{100}{b}\Rightarrow b=100\sqrt{3}$

So, in $△BCD$ (Top View)

$a^2+b^2=d^2\Rightarrow d^2=10000+30000=40000\Rightarrow d=200$