SOLUTION: the ratio of the base of an isosceles triangle to its altitude is 3:4. find the measures of the angles of the triangle.

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Question 925202: the ratio of the base of an isosceles triangle to its altitude is 3:4. find the measures of the angles of the triangle.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a similar triangle:
The altitude splits tat isosceles triangle into two congruent right triangles.
tan%28red%28X%29%29=1.5%2F4=0.375
Looking up the angle that has such a tangent, we find an approximate measure:
red%28X%29=20.556%5Eo (feel free to round that to less decimal places)
So, the angle at the vertex measures 2red%28X%29=2%2A20.556%5Eo=highlight%2841.112%5Eo%29 .
The angles at the base have the same measure, B , and we know that
B%2Bred%28X%29=180%5Eo-->B%2B20.556%5Eo=90%5Eo-->B=90%5Eo-20.556%5Eo-->B=highlight%2869.444%5Eo%29