Thread: 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?

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 be the height that the top of the ladder touches the wall.

By Pythagoras' theorem.

you should be able to take it from there

Hint: the height you can reach is

Ok, from there I have this so far:


(x+7)^2=144-4

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

now what?

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

Originally Posted by suzdisp

Ok, from there I have this so far:


(x+7)^2=144-4

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

now what?

and discard the negative solution.

-Dan

Originally Posted by suzdisp

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

Or if you do it this way then


Use the quadratic formula.

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

-Dan

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?

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

yessssssssss, thank you soooo much for helping me tonight

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

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?