To find the length of the missing leg (let's call it \( b \)) in a right triangle where the other two legs are given as 9.7 km and 9.4 km, we can apply the Pythagorean theorem. The theorem states:
\[ a^2 + b^2 = c^2 \]
Where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the other two legs. Since it's unclear whether the missing leg is one of the two given lengths or if it's the hypotenuse, I'll give solutions for both cases:
Case 1: If the 9.7 km and 9.4 km are the two legs of the triangle.
Using the formula:
\[ (9.7)^2 + (9.4)^2 = c^2 \]
Calculating:
\[ 9.7^2 = 94.09 \] \[ 9.4^2 = 88.36 \] \[ c^2 = 94.09 + 88.36 = 182.45 \] \[ c = \sqrt{182.45} \approx 13.5 \text{ km} \quad \text{(rounded to the nearest tenth)} \]
Case 2: If one of the existing lengths is the hypotenuse and we need to find the other leg.
Assuming \( c = 9.7 \text{ km} \) is the hypotenuse and \( 9.4 \text{ km} \) is one leg:
\[ 9.4^2 + b^2 = 9.7^2 \] Calculating:
\[ 9.4^2 = 88.36 \] \[ 9.7^2 = 94.09 \] \[ 88.36 + b^2 = 94.09 \] \[ b^2 = 94.09 - 88.36 = 5.73 \] \[ b = \sqrt{5.73} \approx 2.4 \text{ km} \quad \text{(rounded to the nearest tenth)} \]
Summary:
- If both given lengths are legs of the triangle, the hypotenuse \( c \) is approximately \( 13.5 \text{ km} \).
- If \( 9.7 \text{ km} \) is the hypotenuse, the missing leg \( b \) is approximately \( 2.4 \text{ km} \).
Make sure to clarify the arrangement of the triangle to determine the correct case!
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