A woman has a ladder that is 13 feet long. If she sets the base of the ladder on level ground 5 feet from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the house?
2006-09-14 14:27:25 · 14 answers · asked by ? 2 in Science & Mathematics ➔ Mathematics
12 feet
Use a^2 + b^2 = c^2
Draw the figure out
5 feet is base. 13 feet is hypotenuse. a is the other side.
a^2 + 5^2 = 13^2
a^2 + 25 = 169
a^2 = 144
a = 12
2006-09-14 14:30:26 · answer #1 · answered by pistonfan1111 1 · 1⤊ 0⤋
Use Pythagorean Theorem: The house can be a, the distance on the ground from the house to the ladder can be b, and the ladder can be c. Using a^2 + b^2 = c^2, you get: a^2 + 25 = 169. Subtract 25 from both sides, then take the square root of both sides, which equals 12.
2006-09-14 21:34:08 · answer #2 · answered by vetgirl77 2 · 0⤊ 0⤋
the ladder makes a right triangle with the ground as the bottom and the house as the side. Since the ladder is opposite the right angle it is the hypotenuse (Side C) Use the pythagoreon theorum ( Asquared plus B squared = C squared) Assume A for the house and B for the ground. Rearrange the equation to solve for A and you get the square root of ( C squared - B squared). Plug in and you get A equals the square root of (13squared - 5squared) the answer is then 12. The ladder reaches 12 feet above the ground.
2006-09-14 21:33:03 · answer #3 · answered by furbags01 2 · 0⤊ 0⤋
The triangle formed by the ladder, the house, and the group would be a RIGHT triangle.
So the Pythagorean Theorem will help you out here.
13 feet is the hypotenuse, the longest side.
13^2 = 5 ^ 2 + ? ^ 2
169 = 25 + ?^2
144 = ? ^ 2 (Subtracted 25)
12 = ?
I only took the positive answer because her ladder is not going underground! Distances are measured in positives only.
2006-09-14 21:36:38 · answer #4 · answered by J G 4 · 0⤊ 0⤋
You asked to show our work, so...
All right triangles share one characteristic: the square of the hypotenuse (the long side) is equal to the sum of the squares of the two short sides (the legs).
We know that the ladder -- the long side -- is 13 feet, and 13 x 13 is 169.
We know that the bottom of the ladder is 5 feet from the wall, and 5 x 5 is 25.
So we have to subtract 25 from 169, and that gives us 144.
Fortunately, 144 is a perfect square -- and it happens to be the square of 12.
So the poster who said 12 is correct, but gets no credit for not showing his work. :-)
Next: answer the same question in hexadecimal...
2006-09-14 21:34:43 · answer #5 · answered by Scott F 5 · 0⤊ 0⤋
Ok, let's see...this is trigonometric combination you need to memorize...5-12-13
Draw a triangle. The hypotenuse is 13 (the length of the ladder), one of the sides is 5 (distance away from the house). You need to solve for the other side of the triangle. Using Pythagoras theorem, you obtain
s^2+h^2 = hypo^2
5^2 + h^2 = 13^2
h^2 = 169-25
h^2 = 144
h = 12
Good luck.
2006-09-14 21:33:25 · answer #6 · answered by alrivera_1 4 · 0⤊ 0⤋
Piston and the other guy is right, using the pythagorean theorem, 13^2=5^2=12^2
Thus, X= 12 Ft.
2006-09-14 21:34:19 · answer #7 · answered by Anonymous · 0⤊ 0⤋
a^2 + b^2 = c^2
a^2 + 5^2 = 13^2
a^2 + 25 = 169
a^2 = 144
a = 12
ANS : 12 feet
2006-09-15 00:36:30 · answer #8 · answered by Sherman81 6 · 0⤊ 0⤋
12 feet from the ground. Use phytogoras theorem.
Buffon, I just could'nt type 13squared, but you had a little more brains than me 13x13.
2006-09-14 21:35:00 · answer #9 · answered by Fadhl 3 · 0⤊ 0⤋
Pythagorus
2006-09-14 21:29:26 · answer #10 · answered by danthemanbrunner 2 · 0⤊ 0⤋