1.

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»

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.


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