Question
Use Pythagorean Theorem to find the missing length of a leg? (1 point) Responses 17.5 17.5 144 144 12 12 225
Answers
Answer
One is 15 the other is 9
Answered by
GPT-4o mini
To use the Pythagorean Theorem to find a missing leg of a right triangle, we need to know the lengths of the other leg and the hypotenuse. The Pythagorean Theorem is stated as:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the legs.
If we are looking for a missing leg (let's say \( b \)), we can rearrange the formula as follows:
\[ b^2 = c^2 - a^2 \]
Then, we take the square root to find \( b \):
\[ b = \sqrt{c^2 - a^2} \]
Since you did not provide the lengths of the hypotenuse or the other leg, I will assume \( a \) and \( c \) have values that correspond to the possible answers you provided: 17.5, 144, 12, and 225.
Let’s assume:
1. \( c = 225 \) (hypotenuse)
2. \( a = 144 \) (one leg)
Now we can calculate \( b \):
\[ b^2 = 225^2 - 144^2 \]
\[ b^2 = 50625 - 20736 \]
\[ b^2 = 29889 \]
\[ b = \sqrt{29889} \]
\[ b ≈ 173 \] (which is not one of the proposed answers)
Next, assume other values and test:
Assume \( c = 144 \) and \( a = 12 \):
\[ b^2 = 144^2 - 12^2 \]
\[ b^2 = 20736 - 144 \]
\[ b^2 = 20692 \]
\[ b = \sqrt{20692} \]
which does not yield any of the answers.
Without specific lengths of the legs or the hypotenuse, I cannot determine the exact missing leg's length. If you can provide those, I'd be glad to help you compute it exactly.
If you have an example where two lengths were already given, please specify those values for accurate assistance.
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the legs.
If we are looking for a missing leg (let's say \( b \)), we can rearrange the formula as follows:
\[ b^2 = c^2 - a^2 \]
Then, we take the square root to find \( b \):
\[ b = \sqrt{c^2 - a^2} \]
Since you did not provide the lengths of the hypotenuse or the other leg, I will assume \( a \) and \( c \) have values that correspond to the possible answers you provided: 17.5, 144, 12, and 225.
Let’s assume:
1. \( c = 225 \) (hypotenuse)
2. \( a = 144 \) (one leg)
Now we can calculate \( b \):
\[ b^2 = 225^2 - 144^2 \]
\[ b^2 = 50625 - 20736 \]
\[ b^2 = 29889 \]
\[ b = \sqrt{29889} \]
\[ b ≈ 173 \] (which is not one of the proposed answers)
Next, assume other values and test:
Assume \( c = 144 \) and \( a = 12 \):
\[ b^2 = 144^2 - 12^2 \]
\[ b^2 = 20736 - 144 \]
\[ b^2 = 20692 \]
\[ b = \sqrt{20692} \]
which does not yield any of the answers.
Without specific lengths of the legs or the hypotenuse, I cannot determine the exact missing leg's length. If you can provide those, I'd be glad to help you compute it exactly.
If you have an example where two lengths were already given, please specify those values for accurate assistance.
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