Providing you know the length of its base and the lengths of its two equal sides, treat it as being two right angled triangles joined together by halving the length of its base.
Then use Pythagoras' theorem to find its height.
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Yes if the isosceles triangle is a right isosceles triangle because that leg opposite the hypotenuse is the height
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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.
The are of any triangle is calculated by the formula: Area = 1/2 x Base x Height
Use Pythagoras' theorem: 82-52 = 39 and the square root of this is 6.244997998 or 6.245 feet in height to 3 d.p.