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A p p e n d i x A : U s e f u l M a t h 721<br />

30˚<br />

d 2 = h<br />

2 + (<br />

d )<br />

2<br />

2<br />

d<br />

h<br />

60˚<br />

d<br />

2<br />

d<br />

2<br />

Figure A.4.5 Height of an equilateral triangle.<br />

rior angles of each is 90 degrees, and we can see (Fig. A.4.6) that, from symmetry, each<br />

of the other two interior angles of either isosceles triangle must be 45 degrees. We can<br />

find the length of the shared side of the two triangles by recognizing that a = b and proceeding<br />

as follows:<br />

2 2 2 2 2<br />

h = a + b or h = 2a<br />

(A.4.9)<br />

45˚<br />

h<br />

45˚<br />

a<br />

h<br />

h = a 2<br />

45˚<br />

45˚<br />

h<br />

2<br />

=<br />

a<br />

2<br />

b = a<br />

Figure A.4.6 Bisecting a square.

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