A 20foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the buildingHow high up the wall does the ladder reach ? (3 points )
The ladder, the wall, and the ground form a right triangle.
Using the Pythagorean theorem,
\(a^2 + b^2 = c^2\),
where \(a\) and \(b\) are the lengths of the two shorter sides of the triangle and \(c\) is the length of the hypotenuse (the ladder).
In this case, \(a = 10\) feet, \(c = 20\) feet (length of the ladder), and we want to find out what \(b\) is.
Substitute the values into the formula:
\(10^2 + b^2 = 20^2\\
100 + b^2 = 400\\
b^2 = 300\\
b = \sqrt{300} = 10\sqrt{3} \text{feet}\).
Therefore, the ladder reaches up the wall to a height of \(10\sqrt{3}\) feet.