Example 1: Triangle \( A B C \) - Given: - Hypotenuse \( A B=10 \mathrm{~cm} \). - One leg \( A C=6 \mathrm{~cm} \). - \(

Ask by Ingram Fernandez. in Guyana

Jan 23,2025

To solve the problem involving triangle \( ABC \), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (\( c \)) is equal to the sum of the squares of the lengths of the other two sides (\( a \) and \( b \)). The formula is given by: \[ c^2 = a^2 + b^2 \] In this case: - The hypotenuse \( AB = 10 \, \text{cm} \) (denote this as \( c \)). - One leg \( AC = 6 \, \text{cm} \) (denote this as \( a \)). - We need to find the length of the other leg \( BC \) (denote this as \( b \)). ### Step 1: Set up the equation Using the Pythagorean theorem: \[ AB^2 = AC^2 + BC^2 \] Substituting the known values: \[ 10^2 = 6^2 + b^2 \] ### Step 2: Calculate the squares Calculating the squares: \[ 100 = 36 + b^2 \] ### Step 3: Solve for \( b^2 \) Rearranging the equation to isolate \( b^2 \): \[ b^2 = 100 - 36 \] Calculating the right side: \[ b^2 = 64 \] ### Step 4: Find \( b \) Taking the square root of both sides to find \( b \): \[ b = \sqrt{64} \] Calculating the square root: \[ b = 8 \, \text{cm} \] ### Conclusion The length of the other leg \( BC \) is \( 8 \, \text{cm} \). Thus, the final answer is: - \( BC = 8 \, \text{cm} \)