Question

GEOMETRY B

Which of these is the length of the hypotenuse of a 30°-60°-90° triangle with legs
measuring 6 in. and 6V3 in.?

Answer 1

Answer: The length of the hypotenuse is 12 inches.

Explanation:

You need to use the Pythagorean Theorem:

`a^2=b^2+c^2`

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

You can say that:

`b=6in\\c=6√(3)in`

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

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

Answer 2

Hypotenuse = 12 inches

Explanation:

As the given triangle involves an angle of 90°, this is a right angle triangle.

We an use the Pythagoras theorem to find the length of hypotenuse

So,

`(H)^2 = (B)^2 + (P)^2\\H^2 = (6)^2 + (6√(3))^2\\ H^2 = 36 + (36*3)\\H^2 = 36 + 108\\H^2 = 144\\√(H^2)=√(144)\\ H=12\ inches`

Hence the length of hypotenuse is 12 inches ..