SOLUTION: An isosceles triangle with an altitude that measures 1.5 feet and congruent sides of 2.5 feet has a perimeter of ...

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Question 965840: An isosceles triangle with an altitude that measures 1.5 feet and congruent sides of 2.5 feet has a perimeter of ...
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the vertex half-angle using the height and side.
cos%28V%2F2%29=1.5%2F2.5
cos%28V%2F2%29=0.6
V%2F2=53.13
V=106.26
The other two angles are found using the sum of the angles,
X%2BX%2BV=180
2X=73.74
X=36.87
Then use the law of sines to find the other side.
sin%28106.26%29%2FY=sin%2836.87%29%2F2.5
Y=2.5%2A%28sin%28106.26%29%2Fsin%2836.87%29%29
Y=4
So the perimeter would be,
P=2.5%2B2.5%2B4
P=9ft