Children climb 8 ft to the top of a slide. The end of the slide is 1 ft above the ground and the slide rises at a 45 degree angle. If the slide makes a straight line from the top to the bottom, how far does a child travel down the slide? Round to the nearest foot.
You have an isosceles triangle with equals sides of 7 foot length. The hypotenuse (which is the slide length) is sqrt(49 + 49) feet. Do the calculation.
To find the distance a child travels down the slide, we can use trigonometry. Since the slide rises at a 45 degree angle, it forms a right triangle with the ground and the slide. The child's vertical climb of 8 ft represents the height of the triangle, and the length we are trying to find represents the hypotenuse.
Now, in a right triangle, the hypotenuse is found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, let's call the length of the hypotenuse (the distance the child travels down the slide) "d." The vertical climb of 8 ft represents one side of the triangle, which we'll call the opposite side. The other side, which represents the distance from the end of the slide to the top, is 1 ft and we'll call it the adjacent side.
Using the Pythagorean theorem, we have:
d^2 = 8^2 + 1^2
d^2 = 64 + 1
d^2 = 65
To find d, we take the square root of both sides:
d = √65
Calculating this, we find that d is approximately 8.06 ft.
Therefore, a child travels approximately 8.06 ft down the slide. Rounded to the nearest foot, the child travels 8 ft down the slide.