Question

Would a 51-foot ladder be long enough to climb a 50-foot wall? Sketch a graph and find your answer using a trigonometric ratio.

Answer 1

Yes , a 51 foot ladder is long enough to climb a 50 foot wall .

Explanation :

The related sketch ( diagram ) is shown in the attached figure .

As per the shown fig , let the angle that the ladder makes with the ground be: =$\theta$

So , we have :

$sin \theta = \frac{Height \hspace3 of \hspace3 wall}{Height \hspace3 of \hspace3 ladder }$

Or,  $sin\theta = \frac{50}{51}$

Or, $\theta = sin^{-1} \frac{50}{51}$

Or ,$\theta = sin^{-1} (0.98) < \frac{\pi}{2}$

Here , since $\theta$ is less the 90° , it means that the ladder is tilted towards the wall touching it at some point .

Hence , the 51 foot ladder is long enough to climb a 50 foot wall.