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Use the information below to find the missing measure such that triangle ABC~ triangle DEF.

AB = 35, DE = 14, DF = 22, Angle A= Angle D = 57 degrees, AC=?

Verified Answer :

If the triangles are similar, DE/DF=AB/AC, so 14/22=35/AC.  Dividing by 7 and simplifying, we have 1/11=5/AC.  Multiplying by 11AC, we see that AC=55.

Louli

Answer:
AC = 55 units

Explanation:
Since we want the two triangles to be similar, therefore, we can apply the similarity ratio.
This ratio is as follows:
\(\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}\)

We are given that:
AB = 35
DE = 14
DF = 22

Substitute with the givens in the above relation to get AC as follows:
\(\frac{AB}{DE} = \frac{AC}{DF} \\ \frac{35}{14} = \frac{AC}{22} \\ AC = 55\) units

Hope this helps :)

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