Question

problem 6: find the length of the missing side for this right triangle. (estimate an irrational answer to two decimal places.) after you enter your answer press go.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( a = 6 \), \( b = 8 \), \( c \) is hypotenuse.

Step2: Substitute values

\( 6^2 + 8^2 = c^2 \) → \( 36 + 64 = c^2 \) → \( 100 = c^2 \)? Wait, no, wait, wait, wait, no, wait, the legs are 6 and 8? Wait, no, wait, 6 and 8, so \( c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \)? Wait, but 10 is rational. Wait, maybe I misread? Wait, the triangle has legs 6 and 8, so hypotenuse is 10. Wait, but the problem says "estimate an irrational answer", but 10 is rational. Wait, maybe the legs are different? Wait, no, the diagram shows legs 6 and 8. Wait, maybe the question is about a different side? Wait, no, it's a right triangle, so if the legs are 6 and 8, hypotenuse is 10. Wait, maybe the problem was miswritten? But according to Pythagorean theorem, \( c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10.00 \).

Answer:

10.00