Question

13 m

12 m
wall
ladder
The ladder, the ground, and the wall form a right triangle.
ground
How far away from the wall does the ladder need to be placed so that it reaches 12 meters up the wall? If needed, ROUND TO THE NEAREST TENTH.
A
17.7 meters
B.
25 meters
С
5 meters
D
313 meters

Answer 1

The ladder needs to be placed at 5 m from the wall.

Explanation:

Pythagoras's Theorem

Being a and b the legs of a right triangle and c its hypotenuse, then

`c^2=a^2+b^2`

The image shows a ladder of length c=13 m as the hypotenuse of the right triangle formed by the height, the ladder, and the ground.

We are given the height up the wall as a=12 m.

We calculate the distance b solving it from the equation above:

`b^2=c^2-a^2`

Substituting:

`b^2=13^2-12^2`

Operating:

`b^2=169-144`

`b^2=25`

Taking the square root:

`b=√(25)`

b = 5 m

The ladder needs to be placed at 5 m from the wall.