a 30 foot ladder is set against the side of a house so that it reaches up 24 feet. if elizabeth grabs the…
a 30 foot ladder is set against the side of a house so that it reaches up 24 feet. if elizabeth grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (the answer is not 21 ft.) round to the nearest tenth of a foot.
Answer
Explanation:
Step1: Find initial base distance
Using Pythagorean theorem (a^2 + b^2 = c^2), where (c = 30) (ladder), (b = 24) (height). Let (a) be base. So (a^2 + 24^2 = 30^2).
(a^2 = 30^2 - 24^2 = 900 - 576 = 324), so (a = \sqrt{324} = 18) feet.
Step2: Find new base distance
Pulled 3 feet farther, so new base (a' = 18 + 3 = 21) feet.
Step3: Find new height
Again use Pythagorean theorem. Let (b') be new height. (21^2 + (b')^2 = 30^2).
((b')^2 = 30^2 - 21^2 = 900 - 441 = 459).
(b' = \sqrt{459} \approx 21.4) feet (rounded to nearest tenth).
Answer:
(21.4) feet