5. c = 13
6. b=6
7. b=8
8. a=30
9. a=2√3
Step-by-step explanation:
We will use Pythagorean theorem in each to find the length of missing side.
[tex]a^2+b^2=c^2[/tex]
5. a=12, b=5
Putting in formula
[tex](12)^2+(5)^2=c^2\\144+25=c^2\\169=c^2\\c^2=169[/tex]
Taking square root on both sides
[tex]\sqrt{c^2}=\sqrt{169}\\c=13[/tex]
Therefore,
c = 13
6. a=8 , c=10
Putting in formula
[tex](8)^2+b^2=(10)^2\\64+b^2=100\\b^2=100-64\\b^2=36\\[/tex]
Taking square root on both sides
[tex]\sqrt{b^2}=\sqrt{36}\\b=6[/tex]
b=6
7. a=15, c=17
Putting in formula
[tex](15)^2+b^2=(17)^2\\225+b^2=289\\b^2=289-225\\b^2=64[/tex]
Taking square root on both sides
[tex]\sqrt{b^2}=\sqrt{64}\\b=8[/tex]
b=8
8. b=40, c=50
Putting in formula
[tex]a^2+(40)^2=(50)^2\\a^2+1600=2500\\a^2=2500-1600\\a^2=900[/tex]
Taking square root on both sides
[tex]\sqrt{a^2}=\sqrt{900}\\a=30[/tex]
a=30
9. b=2 , c=4
Putting in formula
[tex]a^2+(2)^2=(4)^2\\a^2+4=16\\a^2=16-4\\a^2=12[/tex]
Taking square root on both sides
[tex]\sqrt{a^2}=\sqrt{12}\\\sqrt{a^2}=\sqrt{2*2*3}\\a=2\sqrt{3}[/tex]
a=2√3
Keywords: square root, pythagorean theorem
Learn more about square root at:
- brainly.com/question/10382470
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