SOLUTION: Given an isosceles triangle with a height of 4 and a vertex angle of 14.25 degrees, I would like to know a formula to determine the length of the base. Thank you.

Algebra ->  Triangles -> SOLUTION: Given an isosceles triangle with a height of 4 and a vertex angle of 14.25 degrees, I would like to know a formula to determine the length of the base. Thank you.      Log On


   



Question 380320: Given an isosceles triangle with a height of 4 and a vertex angle of 14.25 degrees, I would like to know a formula to determine the length of the base. Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The height bisects the vertex angle and forms a right triangle with (1/2)base as one leg, the height as another leg and the hypotenuse is one of the congruent sides of the isoceles triangle.
.
Since you know the angle,
A=14.25%2F2=7.125
You can use the tangent of the angle to determine the base.
tan%28A%29=OPP%2FADJ=%28%281%2F2%29B%29%2FH=B%2F%282H%29=B%2F8
B=8%2Atan%287.125%29
highlight%28B=1%29