Proposed Problem

Click the figure below to see the complete problem 422 about Triangle, 24, 30 degree, Angle, Congruence.

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Complete Problem 422

Level: High School, SAT Prep, College geometry

## Wednesday, January 27, 2010

### Problem 422: Triangle, 24, 30 degree, Angle, Congruence

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ReplyDeleteIs the answer 48 degrees????

ReplyDeleteThe answer is not 48 degrees

ReplyDeletewith the formula siny=sin(180-y) and the sine rule in ABD and BDC

ReplyDeletesin24.sin(150-x)=sin30.sinx

sin(150-x)=sin(30+x)=sin30.cosx+cos30.sinx

after substitution and division by cosx

we have

tanx=sin30.sin24/(sin30-sin24.cos30)=tan54

x=54

.-.

Here goes again:

ReplyDeletehttp://img218.imageshack.us/img218/4855/solg.png

Antonio: i can't directly copy a link when posting here, why? also, do you have any mail so that i can make you some questions?

Ale:

ReplyDeleteTry to use html tags on your comments:

The HTML for a basic link looks like this:

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Problem 422

ReplyDeleteForming an equilateral triangle ABΕ (D is an interior point of triangle ABE). Then < AEB = 60 = 2.30 = 2.ACB so E is circumcenter of triangle ABC.Therefore AB=BE=AE=EC=DC and

<EAC=36=<ECA, <EDC=72 so <DEA=<DAE=36 then AD=DE. Is triangle ABD=triangle EBD

So <DBA=<DBE=30. Therefore <BDC=x=30+24=54.

APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE