SOLUTION: Please help me solve these problems 1) A rope connecting the top of a pole to the ground is 28yd.long and touches the ground 23yds. from the the pole.How tall is the pole? Round

Algebra ->  Rectangles -> SOLUTION: Please help me solve these problems 1) A rope connecting the top of a pole to the ground is 28yd.long and touches the ground 23yds. from the the pole.How tall is the pole? Round      Log On


   

Question 590806: Please help me solve these problems
1) A rope connecting the top of a pole to the ground is 28yd.long and touches the ground 23yds. from the the pole.How tall is the pole? Round the approximations to the nearest tenth. (My answer 25.5 yd.)
2) If an object is dropped, the distance it falls is given by d=16t^2. Find the distance an object would fall in 8 seconds. (My answer 2048ft)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are x and 23 this means that a=x and b=23


Also, since the hypotenuse is 28, this means that c=28.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2B23%5E2=28%5E2 Plug in a=x, b=23, c=28


x%5E2%2B529=28%5E2 Square 23 to get 529.


x%5E2%2B529=784 Square 28 to get 784.


x%5E2=784-529 Subtract 529 from both sides.


x%5E2=255 Combine like terms.


x=sqrt%28255%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=15.9687 Use a calculator to evaluate the right side


So the height of the pole is approximately 16.0 yards (rounded to the nearest tenth)
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# 2

d=16t%5E2 Start with the given equation


d=16%288%29%5E2 Plug in t=8


d=16%2864%29 Square 8 to get 64


d=1024 Multiply


The object has fallen 1024 feet in 8 seconds.
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