SOLUTION: An isosceles triangle has a base of length 50. The vertex angle measures 27?. What is the perimeter of the triangle?

Question 320075: An isosceles triangle has a base of length 50. The vertex angle measures 27?. What is the perimeter of the triangle?

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Form a right triangle by dropping a line that bisects the vertex angle and bisects the base.
The angle is now bisected and measures 13.5 degrees.
The side opposite to the 13.5 degree angle is half the base or 25.
The side adjacent to the 13.5 degree angle is the height of the triangle.
The sine of 13.5 degrees is equal to 25 divided by the hypotenuse.

The perimeter of the triangle is twice the hypotenuse added to the base.

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