A ladder that is 26 feet long is 10 feet from the base of a wall. How far up the wall does the ladder reach?

Answer 1

24 feet.

use Pythagorean theorem

Answer 2

use the pythagorean theorem.

The pythag. theorem is a^2 + b^2 = c^2 , when a is one leg, b is the other leg and c is the hypotenuse (longest line). The legs make a ninety degree angle, making the pythag. theorem useable. To solve, set up the information:

leg a= floor = feet (10)
leg b= wall = ? (this is the variable you will solve for)
hypotenuse c= ladder = 26

Then set up the equation: (x^2 is x squared, or x to the second power)

10^2 +b^2 = 26^2

Then work out the numbers:

(10)(10) +b^2 = (26)(26)
to
100 + b^2 = 676

Now, use algebra and get the numbers on one side of the equation and the variables on the other. Remember, what you do to one side you do to the other.

100 + b^2 = 676
-100 | -100
to
b^2 = 576

Now, to get the value of b you must get rid of the ^2 part of b^2. Do this by taking the square root. (the square root can be represented by x^(1/2).)

(b^2)^1/2 = 576^1/2

remember; when the equation is (x^c)^b, the rule is => x^c*b
so:

b^2*1/2 = 576^1/2

b^1 = 24 (anything to the power of one is itself)
So

b =24 ; the ladder reaches 24 ft. up the wall

Answer 3

Assuming the wall is perpendicular to the ground, you have a right triangle with the hypotenuse of 26 feet and the base of 10 feet.

Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, your unknown side (the height of the wall where the ladder meets) is x^2 = 26^2 - 10^2, or x^2 = 576, or x=24.

Answer 4

SOH CAH TOA

Sine = Opp/Hyp
Cosine = Adjacent/Hyp
Tangent = Opp/Adjacent

First assume a right triangle is formed and compute the cosine of the angle formed by the hypotenuse (26ft Ladder) and the adjacent side (10ft)

Cos = 10/26 = .3846 = 67.38 degrees

Now that you know the angle formed by the ladder and the distance from the wall. You can use the Tangent of 67.38 degrees to compute the height of the ladder against the wall. This is teh opposite side of the triangle.

Tan of 67.38 = 2.399

rearange the Tan formula (Tan = O/A) to Tan * A = O

2.399 * 10 = 23.99 or 24 feet

Answer 5

The ladder reaches 24 feet up the wall.According to safety awareness the ladder must reach 2 ft above your landing.

Answer 6

use the old A^2 + B^2 = C^2 theorem.

Set the length of the ladder to the hypotenuse (C) = 26 ft, and B to the base (10 ft)... set up and solve for A, the heigth up the wall.

Answer 7

Since it is 26 feet long, and not 26 feet high, then it does not touch the wall... A great trick question !!

Answer 8

Using pythagoras' theroem it is 24ft high Asquared=26squared-10squared Asquared=576 A=Sqaure root of 576 A=24

Answer 9

equation is 26*26=10*10 + X...so square root of 576 is the answer...or 24

Answer 10

24 feet