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The information given represents lengths of sides of a right triangle with c the hypotenuse. Find the correct missing length to the nearest hundredth. A calculator may be helpful.



a = ?, b = 12, c = 19




A.


14.03


B.


14.38


C.


14.73


D.


15.07
please help ASAP

Sagot :

iGreen
Use the Pythagorean Theorem.

a^2 + b^2 = c^2

a^2 + 12^2 = 19^2

Simplify the exponents:

a^2 + 144 = 361

Subtract 144 to both sides:

a^2 = 217

Find the square root of both sides:

a = 14.73
boffeemadrid

Answer:

(C)14.73

Step-by-step explanation:

It is given that c is the hypotenuse, thus using the Pythagoras theorem, we have

[tex]c^{2}=a^{2}+b^{2}[/tex]

Substituting the given values, we have

[tex](19)^2=a^2+(12)^2[/tex]

[tex]361=a^2+144[/tex]

[tex]217=a^2[/tex]

[tex]a=\sqrt{217}[/tex]

[tex]a=14.73[/tex]

Thus, the value of a will be 14.73.

Hence, option (C) is correct.

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