Question

Which of these is the length of the hypotenuse of a 30 60 90 triangle with legs measuring 6in and 6 square root of 3in

Answer 1

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Answer 2

Answer: The length of the hypotenuse is 12 inches.

Step-by-step explanation:

In this case we need to use the Pythagorean Theorem. This is:

$a^2=b^2+c^2$

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

We can say that:

$b=6in\\c=6\sqrt{3}in$

Then, substituting values into $a^2=b^2+c^2$ and solving for "a", we get that the lenght of the hypotenuse is the following:

$a^2=(6in)^2+(6\sqrt{3}in)^2\\\\a=\sqrt{(6in)^2+(6\sqrt{3}in)^2}\\\\a=12in$