A 13-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 9 feet from the base of the building. How high up the wall does the ladder reach?
To find the height up the wall that the ladder reaches, we can use the Pythagorean theorem:
a² + b² = c²
where a = 9 feet (distance from the base of the building to the foot of the ladder), b = height up the wall, and c = length of the ladder (13 feet).
Plugging in the values:
9² + b² = 13²
81 + b² = 169
b² = 88
b = √88
b ≈ 9.38 feet
Therefore, the ladder reaches approximately 9.38 feet up the wall.
A walkway forms one diagonal of a square playground. The walkway is 14 m long. How long is a side of the playground?
In a square, the diagonals form two right triangles. The length of one side of the square can be found using the Pythagorean theorem, where the hypotenuse is the diagonal of the square (14 m) and the legs are each half the side length of the square (s/2).
Using the Pythagorean theorem:
(0.5s)² + (0.5s)² = 14²
0.25s² + 0.25s² = 196
0.5s² = 196
s² = 392
s = √392
s ≈ 19.8 m
Therefore, the length of each side of the square playground is approximately 19.8 meters.