1. ## triangle

Suppose a 12 foot ladder is leaning against a wall so that its base is 2 feet from the edge of the wall. As you climb to the very top of the ladder, you find you can reach 7 feet above the top of the ladder. To what height are you reaching in feet, to one decimal place?

2. Originally Posted by suzdisp
Suppose a 12 foot ladder is leaning against a wall so that its base is 2 feet from the edge of the wall. As you climb to the very top of the ladder, you find you can reach 7 feet above the top of the ladder. To what height are you reaching in feet, to one decimal place?
let $x$ be the height that the top of the ladder touches the wall.

By Pythagoras' theorem. $x^2 = 12^2 - 2^2$

you should be able to take it from there

Hint: the height you can reach is $x + 7$

3. Ok, from there I have this so far:

(x+7)^2=144-4

(x+7)(x+7)=140

now what?

4. to this...
x^2+7x+49=140.
now I'm stuck

5. Originally Posted by suzdisp
Ok, from there I have this so far:

(x+7)^2=144-4

(x+7)(x+7)=140

now what?
$(x + 7)^2 = 140$

$x + 7 = \pm \sqrt{140}$

$x = -7 \pm \sqrt{140}$

-Dan

6. Originally Posted by suzdisp
to this...
x^2+7x+49=140.
now I'm stuck
Or if you do it this way then
$x^2 + 14x - 91 = 0$

(And note the coefficient on the "x" term. You FOILED this wrong.)

-Dan

7. no no no, I hate the quadratic equation. I'll do it your way

so, I get

x=-7 +/- SR 140

x= -7 +/- 11.832159

so, -7 + 11.832159= 4.8 feet?

8. Originally Posted by suzdisp
no no no, I hate the quadratic equation. I'll do it your way

so, I get

x=-7 +/- SR 140

x= -7 +/- 11.832159

so, -7 + 11.832159= 4.8 feet?
Since this is a Math problem I'd use the exact (rather than decimal) answer, but yes, you solved it correctly.

-Dan

9. yessssssssss, thank you soooo much for helping me tonight

10. Originally Posted by suzdisp
yessssssssss, thank you soooo much for helping me tonight
You are welcome, but thank Jhevon. He helped you with the problem, I just helped with solving the equation.

-Dan

11. Originally Posted by suzdisp
Ok, from there I have this so far:

(x+7)^2=144-4

(x+7)(x+7)=140

now what?
where did (x + 7)^2 come from?