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

• A.
• B. 28-48√3
• C.
• D. none of these

Answer 1

The correct option is C

option c

let OA and OB be the paths traveled by the two travelers in 2 hours. Let BC� AO at C. then $\angle$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

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