A right triangle has a leg of 13 cm and a hypotenuse of 21 cm. What is the length of the other leg? Round to the nearest tenth. 8.0 cm 16.5 cm 24.7 cm 272.0 cm pleeeeease help me right "meow"

Question

darkknight · Answer

since this is a right triangle you can use the pythagoreon theorem (a^2+b^2= c^2) c is the hypo and a and b are legs

kittybasil · Answer

As per the Pythagorean Theorem mentioned previous:

"A right triangle has a leg of 13 cm" this can be $a$ or $b$ since both represent leg values. I'm going to use $b$, so $\color{lightcoral}{b=13\text{ cm}}$
"a hypotenuse of 21 cm" which is referred to by $c$, so $\color{plum}{c=21\text{ cm}}$

Now we construct the expression generated by the formula:$$a^2+\color{lightcoral}{b}^2=\color{plum}{c}^2\text{ becomes the following: }a^2+(\color{lightcoral}{13})^2=(\color{plum}{21})^2$$Now let's isolate the variable before we simplify anything.$$a^2\cancel{+13^2\color{lightgreen}{-13^2}}=21^2\color{lightgreen}{-13^2}$$$$a^2=21^2-13^2$$Simplifying, we square these values and get:$$a^2=441-169=272$$Now we solve for $a$ by isolating it. By this, we do:$$\sqrt{a^2}=\sqrt{272}$$$$a=\sqrt{272}$$What answer did you get?

TheSmartOne · Answer

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