A ladder is standing against the wall.if the ladder reaches a height of 12m up the wall and has its foot 5m away from it,calculate the length of the ladder.draw a sketch and show all your calculations
sqrt (5^2+12^2 ) = sqrt(25+144) =sqrt(169) = 13
this is a 5, 12, 13 right triangle
To calculate the length of the ladder, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length 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 forms the hypotenuse of a right-angled triangle, where the height of the ladder against the wall is one side and the distance of the foot of the ladder from the wall is the other side.
Let's use the variables a, b, and c to represent the sides of the triangle, where:
- a is the height of the ladder against the wall (12m)
- b is the distance of the foot of the ladder from the wall (5m)
- c is the length of the ladder
Using the Pythagorean theorem, we have the equation:
c^2 = a^2 + b^2
Substituting the given values, we get:
c^2 = 12^2 + 5^2
c^2 = 144 + 25
c^2 = 169
Now, we take the square root of both sides to solve for c:
c = √169
c = 13
Therefore, the length of the ladder is 13 meters.
To draw a sketch, you can simply draw a right-angled triangle where the vertical side represents the height (12m), the horizontal side represents the distance from the wall (5m), and the hypotenuse represents the length of the ladder (13m). Make sure to label the sides with their corresponding lengths.