Geometry questions

Question

Is either triangle RST or triangle XYZ similar to triangle ABC? ABC has sides 18,27, and 33. Triangle RST has sides 30,40, and 22. XYX has sides 36,24, 44.

Answer 1

Ratio of corresponding sides must be equal so using shortest to longest side ratios 18/33 compared 22/40, cross multiply 18 x 40 = 720; 33x 22 = 726 so triangle RST not similar to triangle ABC

18/33 compared to 24/36 - 18 x 36 = 648; 33 x 24 = 792 so triangle XYZ not similar to triangle ABC

Answer 2

You can solve these triangles by using the Law of Cosines formula.

cos(C) = (a² + b² − c²/ )2ab Angle C = Cos^-1((a² + b² − c²/ )2ab)

cos(A) = (b² + c² − a²/ )2bc " " " " " " " " " " " "

cos(B) = (c² + a² − b² )/2ca " " " " " " " " " " " *

And solving for the angles, all 3 triangles are similar:

17 18 23

22 30 40

24 36 44

50.8° 42.1° 82.1°