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

Answer: It is not long enough.

Explanation:

Ok, we know that the "rule" for the distance between the base of the ladder and the wall is that, for each 4 ft that the ladder rises, we must have 1 foot between the base of the ladder and the wall.

then, for a 50 feet wall, the ladder must rise 50 ft, this means that the base of the ladder must be:

50ft/4 = 12.5 feet away from the wall.

Now, these two values can be thought as the cathetus of a triangle rectangle, and the ladder will be the hypotenuse, then we have (using Pythagoras theorem)

H = √(12.5ft^2 + 50ft^2) = 51.54 ft

So the theoretical safe value is bigger than the one we have, this means that the 51-foot ladder is not long enough.