SOLUTION: The South Memorial School is designing a new playground. There will be a walkway that diagnolly crosses the square playground. The walkway is 55 meters long. Include a sketch of th

Question 958237: The South Memorial School is designing a new playground. There will be a walkway that diagnolly crosses the square playground. The walkway is 55 meters long. Include a sketch of the playground and find the lenght of one side. Round your answer to the nearest 10th.
That's my problem but I can't solve, I don't think it provides enough information. Any one know what to do?
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
You are dealing with a very special triangle, it's called an isosceles right triangle because it has two sides of the same length and two 45 degree angles.
Did you sketch it like the problem asks you to? I did, see below.
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Isosceles right triangles have a special relationship among the sides, 1:1:sqrt2 and one way to find the sides is using the "pattern formula", which applies ONLY to these special triangles:
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Hypotenuse= Leg*sqrt2
But since we want to know the Legs, we divide both sides by sqrt2 and have:
L= H/sqrt2= 1/2H*sqrt2. Since our hypotenuse is 55:
L= 1/2*55*sqrt2= (55*1)/2*sqrt2= 27.5*sqrt2
The square root of 2 is 1.414, so multiply:
27.5*1.414= 38.9 is the length of each side.
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You can also solve it applying trigonometry, remember SOHCAHTOA. Since we know the hypotenuse, let's use CAH (Cosine Adjacent Hypotenuse):
Cos45= L/55 Let's flip the equation, it will look better:
L/55= Cos45 Calculate the cosine of 45 (your calculator):
L/55= 0.707 Multiply both sides times 55
L= 38.9 Oh, what a surprise, we got the same answer both ways ;-)

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