Question
what is the length of the missing leg if necessary round to the nearest tenth 10cm and 6.5cm and a on the right is missing
Answers
GPT-4o mini
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 \( a \):
1. Rearrange the formula to solve for \( a \):
\[
a^2 = c^2 - b^2
\]
2. Substitute the values into the formula:
\[
a^2 = 10^2 - 6.5^2
\]
Calculating the squares:
\[
a^2 = 100 - 42.25
\]
\[
a^2 = 57.75
\]
3. 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.
\[ a^2 + b^2 = c^2 \]
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 \( a \):
1. Rearrange the formula to solve for \( a \):
\[
a^2 = c^2 - b^2
\]
2. Substitute the values into the formula:
\[
a^2 = 10^2 - 6.5^2
\]
Calculating the squares:
\[
a^2 = 100 - 42.25
\]
\[
a^2 = 57.75
\]
3. 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.