Use the sine rule to work out one of the sides.
(a/sina = b/sinb = c/sinc)
Then as it is an isosceles triangle the perpendicular dropped from the apex will (a) bisect the base and (b) form a right angle with the base.
Now you know one side and the hypotenuse of a right-angled triangle and you use Pythagoras (a2 + b2 = c2)
to solve the 'other' side of that, which is the height of the isosceles triangle.
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The sum of the internal angles of a triangle is 180 degrees. If you know the size of the angles at the base of an isosceles triangle, the final angle can be found by subtracting the size of the two known angles from 180.
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Yes! An isosceles triangle has 2 equal sides and two base angles equal.
The are of any triangle is calculated by the formula: Area = 1/2 x Base x Height