To determine which side is the hypotenuse in a triangle, you need to know if it is a right triangle. The hypotenuse is the longest side and is opposite the right angle.
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Identifying the Hypotenuse:
- If the triangle is a right triangle and has one of its angles as 90 degrees (which is not provided in your question), the hypotenuse would be the longest side.
- Since 14.7 km is greater than both x and 11.9 km, if this is a right triangle, then the hypotenuse would be the side labeled 14.7 km.
Response: The side labeled 14.7 km (assuming it is a right triangle).
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Calculating the Value of x:
- If you are trying to find the side \( x \) in a triangle with given sides (11.9 km and 14.7 km), and assuming it is a right triangle, we could use the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.
Let's assume:
- \( c = 14.7 \) km (hypotenuse)
- \( a = 11.9 \) km
- Then, \( b = x \)
The equation becomes: \( 11.9^2 + x^2 = 14.7^2 \)
Calculating:
- \( 11.9^2 = 141.61 \)
- \( 14.7^2 = 216.09 \)
Now, plug them into the equation: \( 141.61 + x^2 = 216.09 \) \( x^2 = 216.09 - 141.61 \) \( x^2 = 74.48 \) \( x = \sqrt{74.48} \) \( x ≈ 8.6 \) km (rounded to the nearest tenth).
Response: 8.6 km.
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