In right triangle $RST$, angle $R$ is the right angle, $S$ is at the top, and $T$ is at the bottom right. If $RS$ = $6$ units and $RT$ = $8$ units, what is the length of side $TS$?

• A. $10$ units
• B. $14$ units
• C. $7$ units
• D. $12$ units

Answer: (A)

Verified step by step guidance

1. Identify the right triangle RST with the right angle at R, meaning sides RS and RT are the legs, and TS is the hypotenuse.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides: \(c^2 = a^2 + b^2\).
3. Assign the given side lengths: \(RS = 6\) units and \(RT = 8\) units, and let \(TS = c\) be the hypotenuse we want to find.
4. Apply the Pythagorean theorem: \(c^2 = 6^2 + 8^2\).
5. Calculate the squares and sum them: \(c^2 = 36 + 64\), then find \(c\) by taking the square root of the sum, \(c = \sqrt{100}\).