SOLUTION: The measure of each base angle of an isosceles triangle is 30, and each of the two congruent sides has length 14. What is the area of the triangle?

Algebra.Com
Question 1185238: The measure of each base angle of an isosceles
triangle is 30, and each of the two congruent sides has
length 14. What is the area of the triangle?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
h = the altitude of the isosceles triangle.
sin(30) = h/14
h = 14 * sin(30) = 14 * 1/2 = 7
cos(30) = (b/2) / 14
b/2 is half the base of the isosceles triangle.
b is the base of the isosceles triangle.
cos(30) = sqrt(3)/2
this gets you:
sqrt(3)/2 = (b/2) / 14
solve for b/2 to get:
b/2 = 14 * sqrt(3)/2 = 7*sqrt(3).
b = 14 * sqrt(3)/2
the area of the isosceles triangle = 1/2 * b * h which is equal to 1/2 * 14 * sqrt(3) * 7 which is equal to 7 * sqrt(3) * 7 which is equal to 49 * sqrt(3).
the area of the triangle is equal to 49 * sqrt(3) square units which is equal to 84.87048957 square units.


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

The measure of each base angle of an isosceles
triangle is 30, and each of the two congruent sides has
length 14. What is the area of the triangle?
Use the formula for the area for any NON-RIGHT triangle: , with ∡ C being the angle between sides "a" and "b". 
∡ C = 180 - 2(30) = 180 - 60 = 120o.

This gives us:

RELATED QUESTIONS

What is the measure of each base angle of an isosceles triangle if its vertex angle... (answered by MathLover1)
What is the measure of each base angle of an isosceles triangle if it's vertex angle... (answered by josgarithmetic)
[ What is the measure of a base angle of an isosceles triangle if the vertex angle... (answered by TimothyLamb)
what is the measure of each base angle of an isosceles triangle if its third angle... (answered by edjones)
What is the measure of each base angle of an isosceles triangle if its vertex angle... (answered by lynnlo)
What is the measure of a base angle of an isosceles triangle if the vertex angle measures (answered by jim_thompson5910)
what is the measure of each base angle of an isosceles triangle if its vertex measures 24 (answered by JBarnum)
what is the measure of each base angle of an isosceles triangle if its third angle... (answered by DrBeeee)
What is the measure of each base angle of an isosceles triangle if it'd vertex angle... (answered by stanbon)