We can take advantage of the symmetry of the isosceles triangle.
By cutting the isosceles triangle in two congruent triangles, each right triangle has a long leg measuring 5.25", (height, H).
The short leg is half the base, K.
Using trigonometry and the definition of tangent, tan(45/2°)=K/H.
=>
K=H*tan(22.5°)=2.187
The base is therefore, 2K, or twice 2.187.
If isosceles angles are 45, 67.5 and 67.5 with a height of 5.25" what is the length of the base?
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