Marsha leans a 6m ladder against a wall. The base of the ladder is 1.5m from the wall. How far up will the ladder reach?
please show how you get the answer.
Answer: 5.8m
2007-05-26 07:04:32 · 9 answers · asked by hello 1 in Science & Mathematics ➔ Mathematics
ill answer this based on my stock knowledge from HS lessons. i stand to be corrected. i believe this is about the pythagorian(?) theorem.
the basics formula: c² = a² + b²
where, c = hypotenus, a = height, b = base
in the problem, the hypotenus and the base are given. so, the answer you gave must be the height. using the formula, this is how it came about...
c (hypotenus) = 6m
a (height) = ?
b (base) = 1.5m
SUBSTITUTE values to the formula:
(6)² = a² + (1.5)²
you will come up with: 36 = a² + 2.25
TRANSPOSE:
36 -2.25 = a²
you will come up with: 33.75 = a²
GET SQUARE ROOTS of both sides:
√33.75 = √a²
you will come up with: 5.81 = a
THEREFORE, a (base) is equal to 5.81 m
*hope i helped! good luck.
2007-05-26 07:24:10 · answer #1 · answered by Kasparov 2 · 0⤊ 0⤋
Pythagorean Theorem problem, assuming the wall is perpendicular to the floor and the floor is level.
The Theorem is; a^2 + b^2 = c^2 where a, b are the legs, those sides that share the right angle, and the hypotenuse, the only other side, is c.
In your problem you are given one leg, the base of the ladder is 1.5m from the wall, and the hypotenuse, the ladder is 6m.Plugging in the numbers gives.
1.5m^2 + b^2 = 6m^2 doing the squaring
2.25m^2 + b^2 = 36m^2 subtracting 2.25m^2 from each side
b^2 = 33.75m^2 taking the square root of each side
b = 5.809475m
Hope this lengthy, but no steps left out, answer will help in other problems of this type.
Doug
2007-05-26 14:47:17 · answer #2 · answered by DOUGLAS M 6 · 0⤊ 0⤋
Use pythagoras theorem.
the ladder against the wall is a right angled triangle with the ladder serving as hypotenuse(c), the base of the ladder (b) and the reach of ladder being the individual sides (a).
so, c^2 = a^2 + b^2
a^2 = c^2 - b^2
= 36 - 2.25 = 33.75
so, a = square root of 33.75
= approx. 5.80 = 5.8m
reach of ladder is 5.8m.
2007-05-26 14:12:58 · answer #3 · answered by ankit41 3 · 0⤊ 0⤋
You need to use the pythagorean theorem. The ladder forms a right triangle with the wall and the ground. The right angle is between the wall and the ground, so the length of one leg is 1.5 and the length of the hypotenuse is 6. You need to solve for the length of the other leg:
x^2 + 1.5^2 = 6^2
x^2 = 33.75 = 5.81
The ladder reaches 5.81 meters up the wall.
2007-05-26 14:12:38 · answer #4 · answered by emp211 3 · 0⤊ 0⤋
Always draw a picture. You have a ladder which is a hypotenuse. One leg is 1.5 meters (ladder base to wall). You want to know the other side. What do you do? Hint, it starts with Phythag.
2007-05-26 14:11:05 · answer #5 · answered by cattbarf 7 · 0⤊ 0⤋
pythagoras.
the ladders length times by itself 6^2=36
length of base times by itself 1.5^2=2.25
height reached 36+2.25 divided by itself=5.8
2007-05-26 14:09:36 · answer #6 · answered by Kevin T 3 · 0⤊ 1⤋
"How far up will the ladder reach?"
Before or after it collapsed because Marsha climbed on it?
2007-05-26 14:21:37 · answer #7 · answered by Anonymous · 0⤊ 0⤋
height = sqrt( (6 m)^2 - (1.5 m)^2)
2007-05-26 14:11:24 · answer #8 · answered by rhino9joe 5 · 0⤊ 0⤋
You need to do your own homework.
2007-05-26 14:08:09 · answer #9 · answered by Alice K 7 · 0⤊ 0⤋