We don’t know which one is the hypotenuse. So if we were to plug it into the Pythagorean theorem, we wouldn’t know where to put it. Two possible answers:
8 squared (copy pasting the symbol here is an inconvenience) + b squared = 10 squared which is 6m after solving.
Or you could say 8 squared + 10 squared = c squared. Solving for C would get us 12.8m as our second possibility.
Two possible values for the length of the third side of a right angle triangle are 6 and [tex]\sqrt{164}[/tex].
" Right angle triangle is a triangle whose one of the interior angle is of 90°."
Formula used
Pythagoras theorem,
(Hypotenuse)² = (Opposite side)² + (adjacent side)²
According to the question,
Two sides of a right triangle measure 10 m and 8 m
Here it is not mentioned 10m and 8m representing which side , that's why this is not enough information to be sure of the length of the third side.
Two possibilities
If Hypotenuse = 10m
Length of one of the side of the right triangle = 8m
Measure of other side 'x' equals to
[tex](10)^{2} = 8^{2} + x^{2}[/tex]
⇒[tex]x^{2} = 100 -64[/tex]
⇒[tex]x^{2} =36[/tex]
⇒[tex]x=6[/tex]
If Hypotenuse is not given then,
(Hypotenuse)² = [tex]10^{2} +8^{2}[/tex]
⇒(Hypotenuse)² = [tex]100 + 64[/tex]
⇒ Hypotenuse = [tex]\sqrt{164}[/tex]
Hence, two possible values for the length of the third side of a right angle triangle are 6 and [tex]\sqrt{164}[/tex].
Learn more about right angle triangle here
https://brainly.com/question/3770177
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