Question

The ramp must be exactly $100$ feet in length and make a ${20}^o$ angle with the level ground. What is the horizontal distance, in meters, from the start of the ramp to the point level with the start of the ramp immediately below the entrance of the mall, rounded to the nearest meter?

Answer 1

Let $AB$ is the ramp which makes a ${20}^{\circ }$ angle with the level ground and $x$ is the distance from the entrance of the mall to the ramp.

Then In Right-angled triangle $ABC$ with angle $A=$ ${90}^{\circ }$

$\therefore \sin B=\frac{AC}{BC}$

$\Rightarrow \cos {20}^{\circ }=\frac{x}{100}$

$1foot=30.48m$

$\Rightarrow x=(30.48\times \cos {20}^{\circ }$)$m$

$\Rightarrow x=30.48\times 0.939$

$\because \cos {20}^{\circ }=0.939$

$\Rightarrow x=28.62m=28.62m$