Question

Solve for x. Round to the nearest tenth, if necessary.

Answer 1

Square root of 19 would be your answer

Answer 2

`\sqrt19`

Explanation:

First we solve for the biggest triangle: using the Pythagorean theorem, (a^2 + b^2 = c^2) we put in the sides,

9^2 + b^2 = 10^2.

solve, 81 + b^2 = 100

then we subtract 81 from both sides. b^2 = 19, and the answer is
`\sqrt 19`.

Now we know what the third side is, which is the hypotenuse for the smaller triangle, so we use the Pythagorean theorem again.

4^2 + x^2 = 19.

Solve

16 + x^2 = 19

Subtract 16 from both sides

x^2 = 19

and finally, we take the square root of both sides

x =
`\sqrt19`