Find the length of x and y in the 30-60-90" triangle. Leave answer in simplest radical form

Question

Right triangle y, x, 6, inside 60

X=? Y=?

Answer x= 3sqrt3 y= 3

Answer 1

In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is the square root of 3 times the length of the shorter leg.

In this case, the shorter leg is x, so the longer leg will be 3x (since it's twice the length of x). We can set up an equation using the Pythagorean Theorem:

x^2 + (3x)^2 = 6^2

Simplifying and solving for x, we get:

10x^2 = 36

x^2 = 3.6

x = sqrt(3.6)

x = sqrt(3 * 1.2)

x = sqrt(3) * sqrt(1.2)

x = sqrt(3) * sqrt(4/3)

x = 2sqrt(3)

So x = 2sqrt(3) or 3.46 (rounded to two decimal places).

To find y, we can use the fact that it's half the length of the hypotenuse, which is 6:

y = 6/2

y = 3

Therefore, x is approximately 3.46 and y is 3.

Answer 2

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