A ladder leaning against a vertical wall is 11.28high up against the wall. The foot of the ladder is 5m from the wall. calculate the length of the ladder please guys answer
Answers
Given:
✰ Height of a vertical wall = 11.28 m
✰ Foot of the ladder from the wall = 5 m
To find:
✠ The length of the ladder.
Solution:
Let's understand the concept first!
- Here in this question first we will assume the length of the ladder as x, the height of a vertical wall and the foot of the ladder from the wall as BC and AC respectively,
- then by using the Pythagoras theorem which states that the square of hypotenuse is equal to the sum of squares of perpendicular and base.
- Thus, using Pythagoras theorem and doing the required calculations, we will find the value of x which is equal to the length of the ladder.
Let's find out...✧
By using Pythagoras theorem,
➤ H² = P² + B²
Here,
- H is the length of the ladder, which we need to find i.e, x.
- P is the height of a vertical wall, i.e, BC.
- B is the foot of the ladder from the wall i.e, AC
➤ AB² = BC² + AC²
➤ x² = 11.28² + 5²
➤ x² = 127.24 + 25
➤ x² = 152.24
➤ x = √152.24
➤ x ≈ 12.34 m
∴ The length of the ladder ≈ 12.34 m
____________________________
The length of the ladder is 11.5 m
FIRSTLY ;
We can solve this problem using Pythagoras theorem and Pythagoras theorem states that,
Square of the hypoteneuse = sum of the square on the other two sides.
with the diagram our hypoteneuse = is the length of our ladder which is not given any length .
HENCE;
We can find the other two sides by squaring the hypoteneuse.
So, LET;
/AC/= HYPOTENEUSE
/BC/ and /AB/ = the other two sides
FURTHERMORE
we can put it in an equation form as said earlier;
Thus;
/AC/ squared = / BC/ + /AB/ all squared
replacing the values, you will find an equation which will involve making your /AC/ the subject by taking the square of /AC/ and taking it with the sum of the two sides .
GOING ONWARDS
You will get your /AC/ which is the length of the ladder to be 11.499 and in one decimal place 11.5 m
