Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 849.

## Sunday, January 27, 2013

### Problem 849: Special Right triangle, Catheti or legs ratio 1:3, 18.5 Degrees, Double angle

Labels:
37-53,
angle,
double angle,
special right triangle

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Is ,AD=DE=EC and EM perpendicular of the AC with EM=AB=c.

ReplyDeleteThen ABME,is ,a parallelogram and ADM is, diagonal. So, angle EBM= angle AEB=β

The triangle DMC is isosceles and rectangular.So,the ABMC , is a cyclic quadrilateral,therefore ,angle AMB=ACB=α.

Βut ,from the triangle ΒΔΜ we ,angle EBM+ angle AMB=α+β=45.

Because (problem 848), β= 26,5 degrees ,then α=18,5 degrees

Image: http://img526.imageshack.us/img526/5597/geogebra3.png

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