Question

A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jack grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 44 ft.) Round to the nearest tenth of a foot.

Answer 1

Answer: 45.8

Step-by-step explanation:

1. Find how far the bottom of the ladder is from the bottom of the house:

(use Pythagorean theorem)

(48)2 (50)2

a2 + 2304 = 2500

-2304 -2304

a2= 196

square root 196 = 14 ( ignore negative root, the length must be positive)

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Then find how far the top of the ladder is from the ground once it is put in its new position:

(20)2 (50)2

a2 + 400 = 2500

-400 -400

a2 = 2100

square root 2100

a = 45.825756

a ≈ 45.8 (round to the nearest tenth)