Problem 13
Answer: Choice C. x = 7*sqrt(2), y = 7
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Explanation:
For any 45-45-90 triangle, the legs are the same length. One leg is 7, so the other leg is 7 as well. This means y = 7.
The hypotenuse of a 45-45-90 triangle is equal to sqrt(2) times the length of either leg. So that leads to 7*sqrt(2) being the hypotenuse. You can use the pythagorean theorem to solve 7^2+7^2 = x^2 to confirm that x = 7*sqrt(2)
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Problem 14
Answer: Choice D. x = 3, y = sqrt(3)
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Explanation:
The hypotenuse is 2*sqrt(3). Take half of this to get sqrt(3), which will be the length of the short leg y. So y = sqrt(3)
Multiply the short leg's length with sqrt(3) to get the length of the long leg
In other words,
long leg = (short leg)*sqrt(3)
long leg = sqrt(3)*sqrt(3)
long leg = sqrt(3*3)
long leg = sqrt(9)
long leg = 3
Therefore, x = 3
All of this applies to 30-60-90 triangles only. Like with problem 13, if you know two sides of a right triangle, you can use the pythagorean theorem to solve for the third missing side.
