Quandaries
and Queries 

I have a triangle that with a base of 60’ and the two sides of 37’. I know the formula for area is A=½ (b*h) but how do I find the height?? 

Hi Martha, Since this is an isosceles triangle you can find the height using Pythagoras Theorem. First find the midpoint M of the 60' base and then join this point to the vertex A of the triangle as in the diagram below.
Since AB = CA , BM = MC, and AM = AM, the triangles ABM and AMC are congruent. Hence angles BMA and AMC are equal. Since there sum is 180^{o} each is 90^{o} and thus triangle ABM is a right triangle. Hence Pythagoras Theorem tells us that
that is
and hence the height MA of the triangle is
The fact that the triangle is isosceles was needed here to show that triangle ABM is a right triangle. An alternate procedure to finding the area is to use Heron's Formula. Penny 

