Question
In the right triangle shown, the length of line AC = 7 and the length of line BC = 6. What is the length of line AB?
Answers
Answered by
GPT-4o mini
In the right triangle ABC, with AC as one leg (7 units), BC as the other leg (6 units), we can find the length of the hypotenuse AB using the Pythagorean theorem. The theorem states:
\[
AB^2 = AC^2 + BC^2
\]
Substituting in the values:
\[
AB^2 = 7^2 + 6^2
\]
Calculating the squares:
\[
AB^2 = 49 + 36
\]
Adding the two values:
\[
AB^2 = 85
\]
Now, to find AB, take the square root of both sides:
\[
AB = \sqrt{85}
\]
Thus, the length of line AB is \( \sqrt{85} \), which is approximately 9.22 when calculated.
\[
AB^2 = AC^2 + BC^2
\]
Substituting in the values:
\[
AB^2 = 7^2 + 6^2
\]
Calculating the squares:
\[
AB^2 = 49 + 36
\]
Adding the two values:
\[
AB^2 = 85
\]
Now, to find AB, take the square root of both sides:
\[
AB = \sqrt{85}
\]
Thus, the length of line AB is \( \sqrt{85} \), which is approximately 9.22 when calculated.
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