Question

pythagorean distance
what is the distance c?
pythagorean formula \\( c^2 = a^2 + b^2 \\)
\\( a = 10 \\), \\( b = 2 \\)

Explanation:

Step1: Identify the formula

We use the Pythagorean theorem: \( c^{2}=a^{2}+b^{2} \), where \( a = 10 \) and \( b = 2 \).

Step2: Substitute values

Substitute \( a = 10 \) and \( b = 2 \) into the formula: \( c^{2}=10^{2}+2^{2} \).

Step3: Calculate the squares

Calculate \( 10^{2}=100 \) and \( 2^{2}=4 \), so \( c^{2}=100 + 4=104 \).

Step4: Find c

Take the square root of 104: \( c=\sqrt{104}\approx10.2 \).

Answer:

\(\sqrt{104}\) (or approximately \( 10.2 \))