Question 590806
# 1


We basically have this triangle set up:



{{{drawing(500,500,-0.5,2,-0.5,3.2,
line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,x),
locate(1,-0.2,23),
locate(1,2,28)
)}}}



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



Remember, the Pythagorean Theorem is {{{a^2+b^2=c^2}}} 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^2+b^2=c^2}}} Start with the Pythagorean theorem.



{{{x^2+23^2=28^2}}} Plug in {{{a=x}}}, {{{b=23}}}, {{{c=28}}} 



{{{x^2+529=28^2}}} Square {{{23}}} to get {{{529}}}.



{{{x^2+529=784}}} Square {{{28}}} to get {{{784}}}.



{{{x^2=784-529}}} Subtract {{{529}}} from both sides.



{{{x^2=255}}} Combine like terms.



{{{x=sqrt(255)}}} 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 <font color="red">16.0 yards</font> (rounded to the nearest tenth)

====================================================================
# 2


{{{d=16t^2}}} Start with the given equation



{{{d=16(8)^2}}} Plug in {{{t=8}}}



{{{d=16(64)}}} Square 8 to get 64



{{{d=1024}}} Multiply



The object has fallen <font color="red">1024 feet</font> in 8 seconds.

<font color="red">--------------------------------------------------------------------------------------------------------------</font>
If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, please consider visiting my website: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Thank you


Jim
<font color="red">--------------------------------------------------------------------------------------------------------------</font>