SOLUTION: in an isosceles triangle, the base is 14 cm long, and the legs are 13 cm long. Find the measure of the vertex angle to the nearest degree

Algebra ->  Triangles -> SOLUTION: in an isosceles triangle, the base is 14 cm long, and the legs are 13 cm long. Find the measure of the vertex angle to the nearest degree      Log On


   

Question 575440: in an isosceles triangle, the base is 14 cm long, and the legs are 13 cm long. Find the measure of the vertex angle to the nearest degree
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The axis altitude (or median) through the vertex splits the vertex angle into two congruent angles and splits the isosceles triangle into two congruent right triangles.

In each of those right triangles the angle at the isosceles triangle vertex is opposite a side measuring 7 cm, while the hypotenuse measures 13 cm.
sin%28ABD%29=7%2F13 --->
So to the nearest degree highlight%28angleABC=65%5Eo%29