Answer:
5. - 27.02
6. - 18.14
8. - 6.24
Step-by-step explanation:
Hello There!
Because each triangle is a right triangle we can solve for the missing side length using the Pythagorean Theorem
The Pythagorean theorem states that the sum of the two legs squared is equal to the hypotenuse squared
[tex]a^2+b^2=c^2[/tex]
For number 5 we are given two legs so all we have to do is plug in the values
[tex]17^2+21^2=c^2[/tex]
now we solve for c
[tex]17^2=289\\21^2=441\\441+289=730\\c^2=730\\\sqrt{c^2} =c\\\sqrt{730} =27.01851217[/tex]
we're left with c = 27.01851217
are final step is to round to the nearest hundredth
So we can conclude that the missing side length is equal to 27.02
For number 6 we are given the hypotenuse and a leg
So this time we use this equation
[tex]a^2=c^2-b^2[/tex]
where a^2 = missing leg
now we plug in the values and solve for a
[tex]a^2=27^2-20^2\\27^2=729\\20^2=400\\729=329\\a^2=329\\\sqrt{a^2} =a\\\sqrt{329} =18.13835715[/tex]
we're left with a = 18.13835715
our final step is to round to the nearest hundredth
So we can conclude that missing side length is equal to 18.14
For number 8 we are given the hypotenuse and a leg
so once again we use this equation:
[tex]b^2=c^2-a^2[/tex]
now we plug in the values and solve for x
[tex]b^2=8^2-5^2\\8^2=64\\5^2=25\\64-25=39\\b^2=39\\\sqrt{b^2} =b\\\sqrt{39} =6.244997998[/tex]
we're left with b = 6.244997998
our final step is to round to the nearest hundredth
so we can conclude that the missing side length is equal to 6.24
