Answer
The ladder reaches a height of 18.33 feet on the wall.
Explanation
The sketch of the ladder and wall is shown below
Noting that the ladder is slanting and is 19 feet long and 5 feet from the base of the wall on the level ground.
Let the height of the ladder on the wall be H feet.
We can see that this setup forms a right angle triangle
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = H
b = 5 feet
hyp = 19 feet
a² + b² = (hyp)²
H² + 5² = 19²
H² + 25 = 361
H² = 361 - 25
H² = 336
H = √336
H = 18.33 feet to the nearest hundredth!
Hope this Helps!!!
