Question
what is the length of the missing leg if necessary round to the nearest tenth 10 mi and 5mi and a on the right is missing
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle, you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse and \( a \) and \( b \) are the other two legs.
From your information, we have:
- One leg \( a = 5 \) mi
- The other leg \( b = 10 \) mi (assuming \( b \) is the leg opposite the missing leg)
Since we need to find the missing leg, we can rearrange the Pythagorean theorem to solve for \( b \):
\[ b^2 = c^2 - a^2 \]
However, without knowing which one is the hypotenuse, we can analyze both cases:
### Case 1: If 10 mi is the hypotenuse:
Here, we have:
- \( c = 10 \) mi
- \( a = 5 \) mi
Using the formula:
\[ b^2 = 10^2 - 5^2 \]
\[ b^2 = 100 - 25 \]
\[ b^2 = 75 \]
\[ b = \sqrt{75} \approx 8.7 \text{ mi} \]
### Case 2: If 5 mi is the hypotenuse:
Here, this case would not make sense since a hypotenuse cannot be shorter than any leg in a right triangle. Thus, it can’t be the case.
### Conclusion:
The length of the missing leg when the hypotenuse is 10 mi and one leg is 5 mi is approximately **8.7 mi** when rounded to the nearest tenth.
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse and \( a \) and \( b \) are the other two legs.
From your information, we have:
- One leg \( a = 5 \) mi
- The other leg \( b = 10 \) mi (assuming \( b \) is the leg opposite the missing leg)
Since we need to find the missing leg, we can rearrange the Pythagorean theorem to solve for \( b \):
\[ b^2 = c^2 - a^2 \]
However, without knowing which one is the hypotenuse, we can analyze both cases:
### Case 1: If 10 mi is the hypotenuse:
Here, we have:
- \( c = 10 \) mi
- \( a = 5 \) mi
Using the formula:
\[ b^2 = 10^2 - 5^2 \]
\[ b^2 = 100 - 25 \]
\[ b^2 = 75 \]
\[ b = \sqrt{75} \approx 8.7 \text{ mi} \]
### Case 2: If 5 mi is the hypotenuse:
Here, this case would not make sense since a hypotenuse cannot be shorter than any leg in a right triangle. Thus, it can’t be the case.
### Conclusion:
The length of the missing leg when the hypotenuse is 10 mi and one leg is 5 mi is approximately **8.7 mi** when rounded to the nearest tenth.