On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the slide and the tire swing is 3 meters and the distance between the tire swing and the monkey bars is 8 meters, how far is the slide from the monkey bars? If necessary, round to the nearest tenth.
Question
On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the slide and the tire swing is 3 meters and the distance between the tire swing and the monkey bars is 8 meters, how far is the slide from the monkey bars? If necessary, round to the nearest tenth.
Solution
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is often written as a^2 + b^2 = c^2.
In this case, the slide, the tire swing, and the monkey bars form a right triangle. The slide and the tire swing are one side of the triangle (3 meters), the tire swing and the monkey bars are another side (8 meters), and the distance between the slide and the monkey bars is the hypotenuse, which we'll call c.
So, we can set up the equation as follows:
3^2 + 8^2 = c^2 9 + 64 = c^2 73 = c^2
To solve for c, we take the square root of both sides:
c = sqrt(73)
So, the distance between the slide and the monkey bars is approximately 8.5 meters when rounded to the nearest tenth.
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