Two travelers start walking from the same point at an angle of 1500 with each

Question

Two travelers start walking from the same point at an angle of 1500 with each other at the rate of 4 kmph and 3 kmph. Find the distance between them after 2 hours

Options:

A . 2

\sqrt{25 + 8 \sqrt{3}}

B . 28-48

\sqrt{3}

C . 2

\sqrt{25 + 12 \sqrt{3}}

D . none of these

Answer: Option C
:
C

option c

let OA and OB be the paths traveled by the two travelers in 2 hours. Let BCÃ¢Â?Â´ AO at C. then $∠$ BOC= 180-150= 30 $^{\circ}$

In right angled triangle OCB, BC= $\frac{6}{2}$ =3 KM and OC= 3 $\sqrt{3}$ km

In right angled triangle ACB, AB $^{2}$ = AC $^{2}$ + BC $^{2}$ = (8+3√3) $^{2}$ +3 $^{2}$ = 100+48 $\sqrt{3}$

AB= 2 $\sqrt{25 + 12 \sqrt{3}}$

Shortcut

$\sqrt{a^{2} + b^{2} - 2 a b c o s α}$ ; α is the angle between the paths a and b between the 2 people. $\sqrt{100 + 48}$ is the answer

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