Question

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

Choices:
• 15 ft
• 7.5 ft
• the square root of 2
• 7.5 multiplied by the square root of 2

Answer 1

I think it is a safe assumption that the ground and the wall are perpendicular. So what kind of triangle is formed with sides of the the top of the ladder to the ground, the bottom of the ladder to the foot of the wall, and the ladder itself?

Answer 2

I've tried dividing 15 by the square root of 2, but the answer I got was 10.61, which, obviously, isn't one of the choices given.

Answer 3

Is it a right triangle with 2 45 degree angles?

Answer 4

Yes. So what does Pythagoras tell us about such a triangle?

Answer 5

That if we have the length of the hypotenuse, we can divide it by the square root of 2 to find the length of the legs. Is that right?

Answer 6

No. Your are going a step too far too fast. First write the basic Pythagorean equation.

Answer 7

Well, okay, yes. But rational what you have got by multiplying the top and bottom by the radical.

Answer 8

Okay.
A squared + B squared = C squared
So, how do I plug my problem into the equation if I only have the length of the hypotenuse?

Answer 9

Oh! So the answer is 7.5 multiplied by the square root of 2?

Answer 10

A = B
So then you have one equation in one unknown

Answer 11

Yes. when you rationalize the denominator it is 2. Which goes 7.4 times into 15.

Answer 12

Thanks so much for the help!

Answer 13

\[\sin \theta =oppo/hypo\]
\[\sin 45=oppo/15\]
\[15 \times (\sin 45)=oppo\]
\[oppo=10.6\]