Determine the size of the angles of a right-angles of a triangle in which the sides are successive terms of an arithmetic sequance.The common difference of the proggression is d=4.
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The three sides of the right triangle are consecutive terms of an arithmetic sequence with common difference 4. If the smallest side is d, the other sides are d + 4 and d + 8. Here, d^2 + (d+4)^2 = (d + 8)^2
=> d^2 + d^2 + 16 + 8d = d^2 + 64 + 16d
=> d^2 - 8d - 48 = 0
=> d^2 - 12d + 4d - 48 = 0
=> d(d - 12) + 4(d - 12) = 0
=> d = -4 and d = 12
d = -4 can be eliminated. This gives the sides of the triangle as 12, 16 and 20.
The angles of the triangle are A and B where sin A = 12/20 = 3/5 or A = 36.86 degrees and sin B = 16/20 = 4/5 or B = 53.13 degrees.
The angles of the triangle are 36.86, 53.13 and 90 degrees.
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