A ladder which is 13m long is made to rest on a vertical pole which is 5m away from the foot of the ladder. How far up the pole is the ladder
Just good ol' Pythagoras.
You might recognize the 5-12-13 right angled triangle, if not
x^2 + 5^2 = 13^2
x^2 = 169 - 25
x^2 = 144
x = √144 = 12
btw, this ladder is not leaning according to standard safety codes
should be appr 4:1, this is 12:5 , great danger of slipping
To find the distance up the pole where the ladder rests, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder represents the hypotenuse of a right triangle, and the distance from the foot of the ladder to the pole represents one of the other two sides. Let's call this distance "a". The height we're looking for is the other side of the triangle, which we'll call "b".
Using the Pythagorean theorem, the equation we can set up is:
a^2 + b^2 = c^2
where a = 5m and c = 13m.
Plugging in the values, we get:
5^2 + b^2 = 13^2
Simplifying:
25 + b^2 = 169
Subtracting 25 from both sides:
b^2 = 144
To solve for b, we take the square root of both sides:
b = √144
b = 12
Therefore, the ladder rests 12m up the pole.