Kali has a 666 meter ladder that she wants to use to get her cat out of a tree. She puts the base of the ladder 222 meters away from the base of the tree.
How high into the tree will the ladder reach?
Round your answer to the nearest tenth of a meter.
We can use the Pythagorean theorem to solve this problem. The ladder, the distance from the base of the tree to the base of the ladder, and the height to which the ladder reaches form a right triangle. The length of the ladder is the hypotenuse, and the distance from the base of the ladder to the base of the tree is one leg of the triangle. Let's call the height to which the ladder reaches the other leg of the triangle.
Using the Pythagorean theorem, we have:
ladder² = distance from base of ladder to base of tree² + height to which ladder reaches²
Substituting the given values, we get:
666² = 222² + height to which ladder reaches²
Simplifying and solving for the height to which the ladder reaches, we get:
height to which ladder reaches = sqrt(666² - 222²) ≈ 621.8 meters
So the ladder will reach a height of about 621.8 meters into the tree. Rounded to the nearest tenth of a meter, the answer is 621.8 meters.