SOLUTION: if the vertex of an isosceles triangle is 80 degrees and the side opposite the vertex measures 12 cm, determine the perimeter of the triangle.

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Question 924424: if the vertex of an isosceles triangle is 80 degrees and the side opposite the vertex measures 12 cm, determine the perimeter of the triangle.
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Make two right triangles from the isosceles triangle by bisecting the vertex angle. The angle is then 40 degrees and the opposite side is 6 cm.
sin%2840%29=OPP%2FHYP=6%2FHYP
HYP=6%2Fsin%2840%29=9.33
The perimeter is then,
P=HYP%2BHYP%2B12
P=9.33%282%29%2B12
P=18.66%2B12
P=30.66cm

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you can solve it this way:
An isosceles triangle can be considered as two right angle triangles joined together so use the tangent ratio to find its altitude h:


given angle B+=80=> angle A+=C=50
base b=12cm
tan%2850+%29+=+h%2F%286cm%29 (where h is the altitude and 6cm is half the base)
tan%2850+%29+=+h%2F%286cm%29
1.1918=+h%2F%286cm%29
1.1918%2A6cm=+h
7.15cm=+h
now we can find a using Pythagorean theorem:
a%5E2=%28b%2F2%29%5E2%2Bh%5E2
a%5E2=%286cm%29%5E2%2B%287.15cm%29%5E2
a%5E2=36cm%5E2%2B51cm%5E2
a%5E2=87cm%5E2
a=sqrt%2887cm%5E2%29
a=9.33cm
P=2a%2Bb (triangle is isosceles, a=c)
P=2%2A9.33cm%2B12cm
P=18.66cm%2B12cm
P=30.66cm