Questions: Find the missing side of the triangle. Round to the nearest tenth if necessary.

Find the missing side of the triangle. Round to the nearest tenth if necessary.
Transcript text: Find the missing side of the triangle. Round to the nearest tenth if necessary.
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Solution

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Solution Steps

Step 1: Identify the Right Triangle and Known Sides

The given triangle is a right triangle with one leg measuring 9 km and the hypotenuse measuring 12 km. We need to find the length of the other leg, denoted as \( x \).

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, \( c = 12 \) km, \( a = 9 \) km, and \( b = x \).

Step 3: Substitute Known Values and Solve for \( x \)

Substitute the known values into the Pythagorean Theorem: \[ 12^2 = 9^2 + x^2 \] \[ 144 = 81 + x^2 \]

Step 4: Isolate \( x^2 \)

Subtract 81 from both sides to isolate \( x^2 \): \[ 144 - 81 = x^2 \] \[ 63 = x^2 \]

Step 5: Solve for \( x \)

Take the square root of both sides to find \( x \): \[ x = \sqrt{63} \] \[ x \approx 7.9 \] (rounded to the nearest tenth)

Final Answer

The length of the missing side \( x \) is approximately 7.9 km.

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