What is the value of angle A and C in degrees ?

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- March 21st 2006, 08:26 AMtotalnewbieTriangle
What is the value of angle A and C in degrees ?

- March 21st 2006, 11:13 AMearbothQuote:

Originally Posted by**totalnewbie**

because AB = BC then AB = BD and BC = BD because the Points A, C, D are points of the semicircle of Thales. B is the centre of this circle.

Triangle ADB is an isosceles triangle, therefore the angle at A has a value of 30°.

The angle at D is a right one. Therefore the angle at C has a value of 60°.

Hope that this helps a little bit.

Greetings

EB - March 21st 2006, 02:33 PMThePerfectHacker
I like the problem :D

I solved it with some trigonometry.

By law of sines we have,

(1)

(2)

Invert (2) to get,

Multiply (1) and (2) to get, remember

Thus,

Thus,

But,

Thus,

Thus,

Thus,

Thus,

- March 22nd 2006, 09:33 AMc_323_h
would this work? i extended some sides and introduced parallel lines to derive the angles. not a very practical way. excuse my sloppy handwriting.