127. Ladder stability: From past mishaps, Seth knows his 16-ft ladder should be leaned against his house in such a
way that the top of the ladder is 6 ft farther above the
ground than the bottom of the ladder is from the base of the
outer wall. With this placement, how far up the side of the
house will the top of the ladder reach?

h = 7.63 ft

Step-by-step explanation:

When a ladder leans against a wall, it forms a right angled triangle. The length of the ladder becomes the hypotenuse of the triangle, while the distance of the bottom of ladder from the wall and the height of top of the ladder from the ground becomes the perpendicular and base, depending upon the selected angle. Using Pythagora's Theorem in this right angled triangle:

Hypotenuse² = Perpendicular² + Base²

where,

Hypotenuse = Length of Ladder = 16 ft

Base = Distance between bottom of ladder and wall = x

Perpendicular = Height of top of of the ladder from ground = x + 6 ft

Therefore,

(16)² = x² + (x + 6)²

256 = x² + x² + 12x + 36

128 = x² + 6x + 18

x² + 6x - 110 = 0

solving the quadratic equation and using positive value:

x = 1.63 ft

So, the height of top of ladder is:

h = 1.63 ft + 6 ft

h = 7.63 ft

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step-by-step explanation:

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