a 15 foot ladder is leaning against a house. The base of the ladder is 4 feet from the house. to the nearest tenth of a foot, how high does the top of the ladder reach?
The ladder and the ground form a right triangle. Use the Pythagorean Theorem to find the other leg of the triangle.
a^2 + b^2 = c^2
a^2 + 4^2 = 15^2
a^2 + 16 = 225
a^2 = 209
a = 14.5 feet
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To find out how high the top of the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, and the distance from the base of the ladder to the house is one of the other sides. Let's call the height at which the top of the ladder reaches "h".
Using the Pythagorean theorem, we can set up the equation:
h^2 = 15^2 - 4^2
Simplifying, we have:
h^2 = 225 - 16
h^2 = 209
Taking the square root of both sides, we find:
h ≈ √(209)
Using a calculator, we get:
h ≈ 14.4
Therefore, to the nearest tenth of a foot, the top of the ladder reaches approximately 14.4 feet.