anonymous
  • anonymous
A wire is stretched from the ground to the top of an antenna tower. The wire is 10 ft long. The height of the tower is 2ft greater than the distance d from the tower's base to the end of the wire. Find the distance d and height of the tower?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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saifoo.khan
  • saifoo.khan
|dw:1328486093894:dw|Using Pythagoras Theorm
saifoo.khan
  • saifoo.khan
\[d^2 + (d+2)^2 = 10^2\]Now solve.
saifoo.khan
  • saifoo.khan
\[d^2 + d^2 + 4d + 4 = 100\] \[2d^2 + 4d -96 = 0\] \[d^2 + 2d - 58=0\]

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More answers

anonymous
  • anonymous
|dw:1328485945617:dw|Apply the pythagorean theorem:\[c^{2} = a^{2}+b^{2}\]\[10^{2} = x^{2}+(x+2)^{2}\]Then solve for x:\[100 = x^{2}+(x^{2}+4x+4)\]\[100 = 2x^{2}+4x+4\]\[0 = 2(x^{2}+2x-48)\]\[0 = x^{2}+2x+48\] \[0 = (x+8)(x-6)\]\[x = -8, 6\]-8 wouldn't work, so x is 6.
saifoo.khan
  • saifoo.khan
Now since x = 6. It means that base is 6. And the height was (d+2) So it means, 6 + 2 = 8
anonymous
  • anonymous
So the distance is 6 ft and the height is 8 ft?
saifoo.khan
  • saifoo.khan
YES!
anonymous
  • anonymous
And you can check it by using the pythagorean theorem:\[6^2 + 8^2 = 10^2\]\[36+64 = 100\]\[100 = 100\]
anonymous
  • anonymous
thank you!!
anonymous
  • anonymous
oh and how do you add those pictures??
saifoo.khan
  • saifoo.khan
Use the "DRAW" tool.|dw:1328486987668:dw|
anonymous
  • anonymous
|dw:1328486943638:dw|
anonymous
  • anonymous
do you guys know how to do this one?
saifoo.khan
  • saifoo.khan
|dw:1328487295843:dw|
saifoo.khan
  • saifoo.khan
It must be a Parallelogram?|dw:1328487359034:dw|Like that?
anonymous
  • anonymous
yes
saifoo.khan
  • saifoo.khan
|dw:1328487518009:dw|Which one is it from these two?
anonymous
  • anonymous
the first one!
saifoo.khan
  • saifoo.khan
Then it's a Trapizium.
anonymous
  • anonymous
so how do I solve it?
saifoo.khan
  • saifoo.khan
So the formula for the are is, \[Area = \frac12 * h * (\text{sum of parallel sides})\]
anonymous
  • anonymous
ok...what else? helppp meee i'm so lost!
saifoo.khan
  • saifoo.khan
Lol. help = 911.
anonymous
  • anonymous
no but really!
saifoo.khan
  • saifoo.khan
Lol. Ok, so \[208 = \frac12 ( 4)(2x-12 + 2x)\]Im sure u can solve now? :D
anonymous
  • anonymous
wait so did you get 8x^2 -24?
anonymous
  • anonymous
I got 29=x^2?
saifoo.khan
  • saifoo.khan
The answer's 29.
anonymous
  • anonymous
thats the length of the two bases?
saifoo.khan
  • saifoo.khan
Nope, since we got the value of "x". we can substitute the value in For the top one, 2x - 12 2(29) - 12 46 For the below one, 2(x) 2(29) 58.
anonymous
  • anonymous
So the total is 104 then? Thank you so much!!
saifoo.khan
  • saifoo.khan
NO! we do not need their sum! We want the values for the Top Side and the Most Bottom Side.
anonymous
  • anonymous
ohhh ok gotcha, so i just separate it with a comma. Like: the lengths of the two bases are 46,58?
saifoo.khan
  • saifoo.khan
YES! :D
anonymous
  • anonymous
it was 57,45???
anonymous
  • anonymous
thanks anyways!!

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