GEOMETRY ………………….?

Emily: GEOMETRY ………………….?
If a 650 cm ladder is placed against a building at a certain angle it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm higher up, how much closer will the ladder be to the building?

I did this on a test and I got the answer 100 cm. What I did was a proportion then cross multiplied but the teacher only gave me half the points. I think I had the right answer but maybe I did the work wrong?…………..

HELP

Answers and Views:

Answer by Diane M
The ladder is making a right triangle with the wall. In the first case, the hypotenuse (the ladder) is 650 cm long and the leg against the wall is 520 cm long. Use the Pythagorean theorem to figure out how far the bottom of the ladder is from the base of the wall. In the next problem, the hypotenuse is still the same but the leg against the wall is now 600 cm long. Use the Pythagorean theorem again to get how far the bottom is from the base, then subtract your two answers.

Proportions absolutely will not work here, as there are no similar figures with which to work. Why you got half credit is beyond me. Honestly, if you stumbled across the right answer this way, I might have given you a single point on the problem, but I’d’ve been tempted to give you nothing at all. You might want to get your teacher a thank-you present.

Answer by MoonRose
Use the Pythagorean theorem a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. In this problem, let’s say the distance between the end of the ladder and the building is a, the height the ladder reaches on the building is b, and c is the length of the ladder. First solve for a.

a^2 + b^2 = c^2
a^2 + 520^2 = 650^2
a^2 = 650^2 – 520^2
a^2 = 152100
a = 390

So the ladder is currently 390 cm away from the building. If it is moved to reach a point that is 80 cm higher, then the height b is now 520+80 = 600 cm. Once again, solve for a. The length of the ladder is still 650 cm.

a^2 + b^2 = c^2
a^2 + 600^2 = 650^2
a^2 = 650^2 – 600^2
a^2 = 62500
a = 250

The ladder used to be 390 cm away from the building and now it is 250 cm away from the building. Thus, the ladder is now 390 – 250 = 140 cm closer to the building than before.

ANSWER: 140 cm