# Hello. how to find the base of an isosceles triangle if the equal sides are given and the angle between them too. for example... Q- find the base of the isosceles triangle if the equal sides are 6 cm each and the angle between them is 45 degree. ( try not to involve trigonometry )

1
by dewanaaryan1
You may use Pythagoras theorem

2014-11-19T04:51:22+05:30

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With out use of sine or cosine of angles, it seems not possible to find it easily.

Let  ABC be the isosceles triangle, with A being the intersection of equal sides. So angle A = 45°.   angles B = C = (180°-45°)/2 = 67.5°.
Given   AB = AC = 6 cm.

The easy way is  :
AB / Sin C = BC / Sin A  = 2 R = circumcircle diameter

=>      BC = AB * Sin A / Sin C  = 2 R * Sin A

BC = base = 6 * Sin 45° / Sin 67.5°  = 4.592  cm
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