To find the length of the missing leg in a right triangle with the other two legs measuring 10 cm and 6.5 cm, we can use the Pythagorean theorem, which states that:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) and \( b \) are the legs of the triangle,
- \( c \) is the hypotenuse.
Assuming that 10 cm is the hypotenuse \( c \), and 6.5 cm is one of the legs \( b \), we can solve for the missing leg \( a \):
- Rearrange the formula to solve for \( a \):
\[ a^2 = c^2 - b^2 \]
- Substitute the values into the formula:
\[ a^2 = 10^2 - 6.5^2 \]
Calculating the squares:
\[ a^2 = 100 - 42.25 \] \[ a^2 = 57.75 \]
- Now, take the square root to find \( a \):
\[ a = \sqrt{57.75} \approx 7.6 \text{ cm} \]
Thus, the length of the missing leg is approximately \( 7.6 \) cm when rounded to the nearest tenth.
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