Can someone explain to me how to get two lengths of a triangle.
one triangle has on side ab has a length of 27 a length of 40 on side bc and a length of 18 for the base which will be ac, then on the next triangle you de with a length of 18 ef length is not known and length of df is not known. how do i figure out the lengths

Step-by-step explanation:

Name the vertices of the first triangle A, B, C, starting from lower left and working clockwise. Name the vertices of the second triangle D, E, F, starting from lower left and working clockwise.

If sides a, b, c are the sides opposite angles A, B, C, and the sides d, e, f are apparently the sides opposite angles D, E, F, you seem to have

... a = 40, b = 18, c = 27

... f = 18

There's probably something about the problem statement or picture that tells you the triangles are similar. This might be marking of the angles, or a similarity statement like ΔABC ~ ΔDEF. If there's no such indication, the problem cannot be worked.

The fact that the triangles are similar means the sides of one are proportional in length to the sides of the other. The constant of proportionality can be figured from the sides whose length is given.

The vertices correspond according to the similarity statement (either the one given or the one you determine based on the drawing). Here, we have assumed ΔABC ~ ΔDEF, so DE/AB = DF/AC = EF/BC. Filling in numbers, you have ...

  18/27 = DF/18 = EF/40

Then DF = 18·2/3 = 12

and EF = 40·2/3 = 26 2/3

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