find the length of the hypotenuse of the triangle in the coordinate plane.
find the length of the hypotenuse of the triangle in the coordinate plane.
Answer
Explanation:
Step1: Determine the lengths of the two legs
From the coordinate plane, one leg (horizontal) has a length of (8) units (from ((0,0)) to ((8,0))), and the other leg (vertical) has a length of (2) units (from ((8,0)) to ((8,2))).
Step2: Apply the Pythagorean theorem
The Pythagorean theorem is (a^{2}+b^{2}=c^{2}), where (a = 8), (b=2), and (c) is the hypotenuse. Substitute the values: (8^{2}+2^{2}=c^{2}) [ \begin{align*} 64 + 4&=c^{2}\ 68&=c^{2} \end{align*} ] Take the square root of both sides: (c=\sqrt{68}) Simplify (\sqrt{68}=\sqrt{4\times17} = 2\sqrt{17}\approx 8.25)
Answer:
The length of the hypotenuse is (2\sqrt{17}\approx8.25) units.