Question

For the following right triangle, find the side length X. round to nearest hundredth

Answer 1

Answer:

12.04

Step-by-step explanation:

Hello

Pythagoras' theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the side lengths

$(side)^{2} +(side)^{2} =(hypotenuse)^{2}$

Step 1

isolate

in this case we know a side, and the hypotenuse,so we must isolate a side,

$(side)^{2} +(side)^{2} =(hypotenuse)^{2}\\(side)^{2} =(hypotenuse)^{2}-(side)^{2}\\side=\sqrt{(hypotenuse)^{2}-(side)^{2}$

if you are finding a distance, take only the positive root, talking about negative distances makes no sense

Step 2

put the values into the equation

$let\\side=12\\hypotenuse=17 \\side_{2}=? \\ \\side_{2}=\sqrt{(hypotenuse)^{2}-(side)^{2}}\\ \\side_{2}=\sqrt{(17)^{2}-(12)^{2}}\\side_{2}=\sqrt{289-144}\\side_{2}=\sqrt{145} \\side_{2}=12.04$

side= 12.04 units

Answer 2

For this problem, you will need to use the pythagorean theorem which is $a^{2} + b^{2} = c^{2}$ 
So a and b are usually the sides that are NOT the hypotenuse, or in this case the long side that is not at a 90 degree angle.
You will start by plugging 12 into with (a) or (b) but not both. And then you will plug 17 in for (c). Make sure you square these values to solve the equation. Once you do that, it is basic algebra from there to solve for the missing variable. If you want to check to see if your answer is correct, then plug all the side numbers back into the equation. Also your answer should be between 12 and 17, or possibly one of those numbers.