perplexus.info :: Shapes : Angle Ratio Ascertainment 5

Angle Ratio Ascertainment 5 (Posted on 2016-08-06)

Consider triangle EFG with ∠EGF=90^o
ET is drawn parallel to FG, such that
T and F are located on opposite sides of EG, and
FT intersects EG at S, and
ST = 2EF

Find ∠EFG/∠SFG

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

| Comment 1 of 2

The puzzle is quite simple if seen the right way.

Consider the triangle EFT. For the law of the sines:

ET/sin(EFT) = EF/sin(ETF)

ET=TS cos(ETS) =2EF cos(ETS)

From here: 2EF cos(ETS) sin(ETF)= EF sin(EFT)

but ETF=ETS

Then: 2 cos(ETS) sin(ETS) = sin(EFT); sin(2ETS) = sin(EFT)

ETS= EFT/2 (angles)

The puzzle asks for the ratio EFG/SFG

EFG=EFS + SFG = EFT + ETS = 3ETS =3SFG

Then EFG/SFG=3

/ °|

/ ° |

/_E_____°_ |G

| S °

| °

|° T

Edited on August 9, 2016, 10:40 am

Posted by armando on 2016-08-09 04:31:42

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