Questions: Find the length of the missing side. If necessary, round to the nearest tenth.

Transcript text: Find the length of the missing side. If necessary, round to the nearest tenth.

Solution

Solution Steps

Step 1: Identify the given values and the unknown

We are given a right triangle with one leg measuring 34 units, the hypotenuse measuring 38 units, and we need to find the length of the other leg, denoted as \( b \).

Step 2: Apply the Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (\( c \)) is equal to the sum of the squares of the other two sides (\( a \) and \( b \)): \[ c^2 = a^2 + b^2 \] Here, \( c = 38 \) and \( a = 34 \). We need to find \( b \).

Step 3: Substitute the known values into the equation

\[ 38^2 = 34^2 + b^2 \] \[ 1444 = 1156 + b^2 \]

Step 4: Solve for \( b^2 \)

\[ b^2 = 1444 - 1156 \] \[ b^2 = 288 \]

Step 5: Find the square root of \( b^2 \)

\[ b = \sqrt{288} \] \[ b \approx 16.97 \]