Step-by-step explanation:
![R(r_1+r_2)=r_1r_2\qquad\text{divide both sides by}\ (r_1+r_2)\neq0\\\\\large\boxed{R=\dfrac{r_1r_2}{r_1+r_2}}](https://tex.z-dn.net/?f=R%28r_1%2Br_2%29%3Dr_1r_2%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%7D%5C%20%28r_1%2Br_2%29%5Cneq0%5C%5C%5C%5C%5Clarge%5Cboxed%7BR%3D%5Cdfrac%7Br_1r_2%7D%7Br_1%2Br_2%7D%7D)
Answer:
Step-by-step explanation:
Since this is a 30-60-90 triangle, we need the Pythagorean triple for such a triangle. the side length across from the 30 degree angle is labeled as x, the side across from the 60 degree angle is x√3, and the hypotenuse is 2x. Since we know the side length of the side across from the 60 degree angle, we use that identity and solve for x:
and
and rationalizing the denominator,
![x=\frac{18}{\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }=\frac{18\sqrt{3} }{3}=6\sqrt{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B18%7D%7B%5Csqrt%7B3%7D%20%7D%2A%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B%5Csqrt%7B3%7D%20%7D%3D%5Cfrac%7B18%5Csqrt%7B3%7D%20%7D%7B3%7D%3D6%5Csqrt%7B3%7D)
This is the side length of the side across from the 30 degree angle. In order to find the hypotenuse, we have to multiply this value by 2 to get
12√3, the third choice down.
Answer:
commutative property of multiplication
Step-by-step explanation: