Question

Mr. Chacko of the Padyatra Party wanted to go from Delhi to Dehradun. The party travelled 150 km straight and then took a ${45}^{\circ }$ turn towards Varanasi and walked straight for another 120 km. Approximately how far was the party from the starting point?

• A. 250 km
• B. 90 km
• C. 30 km
• D. 192 km

Answer 1

The correct option is A

250 km

Let O be the starting point of the party.


OA = 150km, AC = 120 km

$In\Delta ABC,sin{45}^{\circ }=\frac{BC}{AC}\frac{1}{\sqrt{2}}=\frac{BC}{120}\Rightarrow BC=60\sqrt{2}andcos{45}^{\circ }=\frac{AB}{AC}\Rightarrow \frac{1}{\sqrt{2}}=\frac{AB}{120}\Rightarrow AB=60\sqrt{2}\therefore OB=OA+AB=150+60\sqrt{2}\Rightarrow OB=150+60\left(1.414\right)=234.84andBC=60\sqrt{2}=60\left(1.414\right)=84.84$

In $\Delta OBC,O{C}^2=O{B}^2+B{C}^2$
$\Rightarrow O{C}^2=(234.84{)}^2+(84.84{)}^2$
$\Rightarrow O{C}^2=55149.82+7197.82$
$\Rightarrow O{C}^2=62347.64$
$\Rightarrow OC=\sqrt{62347.64}=249.69$
$\therefore$ OC = 250 km (approx)
Thus, the distance between starting point to the final point is 250 km approx.