Question 378531: The vertex angle of an isosceles triangle is 62. If the length of the base if 22. How long are the legs? Found 2 solutions by richard1234, robertb:Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! Suppose the vertices of the triangle are A,B,C such that AB = 22, angle C = 62 degrees (this will make labeling much easier). It follows that angle A = angle B = 59. By the law of sines,
Solving, we find AC = BC = = 21.357...
You can put this solution on YOUR website! Draw the altitude from the top vertex to the base of the triangle. Then two congruent right triangles will form, one angle being 31 degrees (half of 62 degrees), and opposite it a side measuring 11 units. The hypotenuse, which corresponds to the leg of the isosceles triangle, is c . Hence . Then .
