Question

GEOMETRY B

Answer 1

Answer: The length of the hypotenuse is 12 inches.

Step-by-step 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:

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

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

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

Answer 2

Answer:

Hypotenuse = 12 inches

Step-by-step 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,

$(H)^2 = (B)^2 + (P)^2\\H^2 = (6)^2 + (6\sqrt{3})^2\\ H^2 = 36 + (36*3)\\H^2 = 36 + 108\\H^2 = 144\\\sqrt{H^2}=\sqrt{144}\\ H=12\ inches$

Hence the length of hypotenuse is 12 inches ..