A right triangle has one leg measuring $18\mathrm{mm}$ and a hypotenuse measuring $24\mathrm{mm}$. What is the length of the missing leg?

• A. $16\mathrm{mm}$
• B. $18\mathrm{mm}$
• C. $32\mathrm{mm}$
• D. $26\mathrm{mm}$

Answer: (A)

Verified step by step guidance

1. Identify the given elements of the right triangle: one leg measures 18 mm and the hypotenuse measures 24 mm.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b): \(c^2 = a^2 + b^2\).
3. Assign the known values: let the missing leg be \(b\), the known leg be \(a = 18\) mm, and the hypotenuse be \(c = 24\) mm. Substitute these into the Pythagorean theorem: \$24^2 = 18^2 + b^2$.
4. Rearrange the equation to solve for the missing leg \(b\): \(b^2 = 24^2 - 18^2\).
5. Calculate the right side of the equation to find \(b^2\), then take the square root of that result to find the length of the missing leg \(b\).