SOLUTION: An isoceles triangle has congruent sides that each measure 3 feet and a base angle of measure of x as shown in the sketch. The third side has a whole number length, if x <60 degree

Question 969688: An isoceles triangle has congruent sides that each measure 3 feet and a base angle of measure of x as shown in the sketch. The third side has a whole number length, if x <60 degrees , what are the possibilities of the perimeter of the triangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
v, the vertex angle.

One objective is to find a formula for the base length.
b, the length of the base.
Law of Cosines:

-----Think or inspect this angle on The Unit Circle.

.... .

Revise the equation for .

The isosceles triangle to have any meaning and match the given requirement, .

Perimeter:

, again refer to Unit Circle to see.

Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!
An isoceles triangle has congruent sides that each measure 3 feet and a base angle of measure of x as shown in the sketch. The third side has a whole number length, if x <60 degrees , what are the possibilities of the perimeter of the triangle?

Third side's length is a whole number
Third side's length > 0, but < 6
Third side is the longest side
Third side's length > 3 feet
Therefore, third side can either be 4 or 5
Thus, perimeter is either: feet
RELATED QUESTIONS
An isosceles triangle has congruent sides that each measure 3 feet and a base angle of... (answered by josgarithmetic)
An isoceles triangle has a perimeter of 45cm. Its equal sides each measure 6cm longer... (answered by jojo14344)
[ What is the measure of a base angle of an isosceles triangle if the vertex angle... (answered by TimothyLamb)
if two base angles of an isoceles triangle are equal in measure and the third angle is... (answered by ankor@dixie-net.com)
What is the measure of each base angle of an isosceles triangle if it'd vertex angle... (answered by stanbon)
If each base angle of an isoceles triangle measures 55degrees,find the measure of the... (answered by sarah_adam)
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 third angle... (answered by MRperkins)
What is the measure of each base angle of an isosceles triangle if its vertex angle... (answered by Fombitz)