a) missing side = 14.4 inches
b) missing side = 8.9 inches
Step-by-step explanation:
A right angled triangle has 3 sides; hypotenuse (the longest side) and 2 lengths.
a) DATA
Length of one side: 8 inches
Length of second side: 12 inches
Length of hypotenuse: c
You will use formula of Pythagoras theorem to solve this
Pythagoras theorem: [tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
a = 8
b = 12
c = ?
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
[tex]c^{2}[/tex] = [tex]8^{2}[/tex] + [tex]12^{2}[/tex]
[tex]c^{2}[/tex] = 208
c = [tex]\sqrt{208}[/tex]
c = 14.4 inches
Therefore, the missing side is equal to 14.4 inches.
b) DATA
Length of one side: 8 inches
Length of second side: b
Length of hypotenuse: 12 inches
You will use formula of Pythagoras theorem to solve this
Pythagoras theorem: [tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]
a = 8
b = x
c = 12
[tex]12^{2}[/tex] = [tex]8^{2}[/tex] + [tex]b^{2}[/tex]
[tex]12^{2}[/tex] - [tex]8^{2}[/tex] = [tex]b^{2}[/tex]
[tex]b^{2}[/tex] = 80
b = [tex]\sqrt{80}[/tex]
b = 8.9 inches
Therefore, the missing side is 8.9 inches.
Keyword: Right triangle, Pythagoras
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