Dear Jiskha,
I will appreciate if you can show me step by step how this geometry math question is solved.
Using the Pythagorean Theorem,how do i find the length the unknown side 'b'.
Side 'a' has a measurement of 1...the hypotenuse: a square root of 2.
Your help is appreciated.
hypot^2=b^2 + 1^2
or
sqrt2 )^2=b^2+1
b^2=2-1
b=1
To find the length of the unknown side 'b' using the Pythagorean Theorem, follow these steps:
Step 1: Identify the known sides of the right triangle.
In this case, side 'a' has a measurement of 1 and the hypotenuse has a measurement of √2.
Step 2: Write down the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. It can be written as:
c^2 = a^2 + b^2
where 'c' represents the length of the hypotenuse, 'a' represents the length of one known side, and 'b' represents the length of the other known side.
Step 3: Plug in the known values into the equation.
In this case, the length of the hypotenuse is √2 and the length of side 'a' is 1. Plug these values into the Pythagorean Theorem equation:
(√2)^2 = 1^2 + b^2
Step 4: Simplify the equation.
Squaring √2, 1, and eliminating the parentheses gives:
2 = 1 + b^2
Step 5: Isolate the unknown variable.
Subtract 1 from both sides of the equation:
2 - 1 = b^2
1 = b^2
Step 6: Solve for 'b'.
To find the length of 'b', take the square root of both sides of the equation:
√1 = √b^2
1 = b
Therefore, the length of the unknown side 'b' is 1.