Since this is a 30-60-90 right triangle, we know that the sides exist in the proportion 1:3‾√
:2. The shortest side, 1, is opposite the 30 degree angle. Since side X is opposite the 60 degree angle, we know that it is equal to 1∗3‾√
Or about 1.73. Finally, side Y is opposite the right angle, and it is twice the shortest side, or 2.
Answer:
37 units
Step-by-step explanation:
![\boxed{distance = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }}](https://tex.z-dn.net/?f=%5Cboxed%7Bdistance%20%3D%20%20%5Csqrt%7B%28x2%20-%20x1%29%5E%7B2%7D%20%2B%20%28y2%20-%20y1%29%5E%7B2%7D%20%20%7D%7D)
Using the distance formula above,
distance between (15, -17) and (-20, -5)
![= \sqrt{[15 - ( - 20)]^{2} + [ - 17 - ( - 5)] {}^{2} } \\ = \sqrt{(15 + 20)^{2} + ( - 17 + 5)^{2} } \\ = \sqrt{35 ^{2} + ( - 12) {}^{2} } \\ = \sqrt{1225 + 144} \\ = \sqrt{1369} \\ = 37 \: units](https://tex.z-dn.net/?f=%20%3D%20%20%5Csqrt%7B%5B15%20-%20%28%20-%2020%29%5D%5E%7B2%7D%20%20%2B%20%5B%20-%2017%20-%20%28%20-%205%29%5D%20%7B%7D%5E%7B2%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%2815%20%2B%2020%29%5E%7B2%7D%20%2B%20%28%20-%2017%20%2B%205%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B35%20%5E%7B2%7D%20%2B%20%28%20-%2012%29%20%7B%7D%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B1225%20%2B%20144%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B1369%7D%20%20%5C%5C%20%20%3D%2037%20%5C%3A%20units)
Ohhh man, I've come across a similar question and I'm stuck, too. Try going to Yahoo, they always have something useful up their sleeves.