I have to find the area of an isoceles triangle with one angle side of 30 degrees, and length of base 5. Could you please help me solve this problem?
I drew a diagram of an isosceles triangle with a 30o angle at B, and hence also at C. Th base BC has length 5.
D is the midpoint of BC so angle BDA is a right angle. Hence triangle ABD is a 30-60-90 triangle. You can use trigonometry to find the length of AD but I remember that in a 30-60-90 triangle the sides are in the proportions 1:2:root(3). Thus BD is root(3) times as long as AD. |BD| = 2.5 and hence |AD| = 2.5/root(3). |AD| is the height of the triangle ABC and hence you can find its area. Cheers,
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