Question

On a flat road, a company needs to construct a flyover for smooth traffic. The flyover will be at an angle of ${37}^0$ to the flat road. The road leading up to the flyover and back down to the flat road are each of $50m$. The horizontal part of the flyover will be $100m$ in length. Find the length (in $m$) of the old road on which this flyover construction is scheduled.

Answer 1

In the question, AD = BC = 50 m, CD = 100 m, Angle DAX = angle CBY = 37.

To find- AB

In triangle AXD

$\cos 37=\frac{DX}{AD}\frac{4}{5}=\frac{DX}{50}DX=40$

Similarily in triangle YBC,

BY = 40 m

So, AB = 40+100+40 = 180 m

So, the answer is 180 m