## anonymous 4 years ago 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?

1. saifoo.khan

|dw:1328486093894:dw|Using Pythagoras Theorm

2. saifoo.khan

$d^2 + (d+2)^2 = 10^2$Now solve.

3. saifoo.khan

$d^2 + d^2 + 4d + 4 = 100$ $2d^2 + 4d -96 = 0$ $d^2 + 2d - 58=0$

4. 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.

5. saifoo.khan

Now since x = 6. It means that base is 6. And the height was (d+2) So it means, 6 + 2 = 8

6. anonymous

So the distance is 6 ft and the height is 8 ft?

7. saifoo.khan

YES!

8. anonymous

And you can check it by using the pythagorean theorem:$6^2 + 8^2 = 10^2$$36+64 = 100$$100 = 100$

9. anonymous

thank you!!

10. anonymous

oh and how do you add those pictures??

11. saifoo.khan

Use the "DRAW" tool.|dw:1328486987668:dw|

12. anonymous

|dw:1328486943638:dw|

13. anonymous

do you guys know how to do this one?

14. saifoo.khan

|dw:1328487295843:dw|

15. saifoo.khan

It must be a Parallelogram?|dw:1328487359034:dw|Like that?

16. anonymous

yes

17. saifoo.khan

|dw:1328487518009:dw|Which one is it from these two?

18. anonymous

the first one!

19. saifoo.khan

Then it's a Trapizium.

20. anonymous

so how do I solve it?

21. saifoo.khan

So the formula for the are is, $Area = \frac12 * h * (\text{sum of parallel sides})$

22. anonymous

ok...what else? helppp meee i'm so lost!

23. saifoo.khan

Lol. help = 911.

24. anonymous

no but really!

25. saifoo.khan

Lol. Ok, so $208 = \frac12 ( 4)(2x-12 + 2x)$Im sure u can solve now? :D

26. anonymous

wait so did you get 8x^2 -24?

27. anonymous

I got 29=x^2?

28. saifoo.khan

29. anonymous

thats the length of the two bases?

30. 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.

31. anonymous

So the total is 104 then? Thank you so much!!

32. saifoo.khan

NO! we do not need their sum! We want the values for the Top Side and the Most Bottom Side.

33. anonymous

ohhh ok gotcha, so i just separate it with a comma. Like: the lengths of the two bases are 46,58?

34. saifoo.khan

YES! :D

35. anonymous

it was 57,45???

36. anonymous

thanks anyways!!