a ladder 15 feet long leans against the wall and forms an angle of 45 degrees with the ground. how far from the wall is the ladder?

Question

whpalmer4 · Answer

|dw:1372366487422:dw| use Pythagorean theorem...

whpalmer4 · Answer

smart-alec answer: "it's touching!" :-)

austinl · Answer

darn it, you beat me to the drawing.

whpalmer4 · Answer

presumably the problem really wants to know the distance the base of the ladder is from the wall...

austinl · Answer

You could also use SohCahToa as well, I actually prefer that method. but your way should give an exact answer.

anonymous · Answer

i did the therom and i cant get the answer still

austinl · Answer

$$h^2+h^2=c^2$$
From that you should be able to solve for h, which is the distance from the ladder to the wall.

whpalmer4 · Answer

Pythagorean theorem says the sum of the squares of the sides = the square of the hypotenuse.  Here we have the hypotenuse = 15, and the two sides are equal (because the 45 degree angle implies an isosceles triangle).
$$h^2 + h^2 = 15^2$$$$2h^2 = 225$$$$h = \sqrt{225}/\sqrt{2} = $$

whpalmer4 · Answer

it is worth remembering that the ratio of the sides in a right isosceles triangle is $1:1:\sqrt{2}$

whpalmer4 · Answer

so one could just write down the answer immediately as $15/\sqrt{2}$ or $15\sqrt{2}/2$

austinl · Answer

Very nice work sir! Kudos.

whpalmer4 · Answer

@minxgirl did you figure out where you went amiss?