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Use Cosine Rule

a^(2) = b^(2) + c^(2) - 2bcCosA

Algebrically rearrange

CosA = [a^(2) - b^(2) - c^(2)] / -2bc

Substitute

CosA = [13^(2) - 12^(2) - 5^(2)# / -2(12)(5)

CosA = [ 169 - 144 - 25] / -120

Cos)A) = [0] / -120

CosA = 0

A = 90 degrees (the right angle opposite the hypotenuse)/

However,

If 'A' is the angle between '12' & '13' then 'a' is the side '5'

Hence (Notice the rearrangement of the numerical values).

CosA = [5^(2) - 12^(2) - 13^(2) ] / -2(12)(13)

CosA = [ 25 - 144 -169] / -312

CosA = [ -288[/-312

CosA = 288/312

A = Cos^(-1) [288/312]

A = 22.61986495.... degrees.

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lenpollock

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4d ago

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More answers

The answer depends on which of the three angles 'a' is!

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Wiki User

10y ago
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Q: What is the cos of angle 'a' with the measurements 5 13 12?
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What is the sin of angle B if the angles are 5 12 and 13?

This is a classic Pythagorean triangle. Although you have given the side lengths, you have NOT given a letter to correspond , with the given side. However, Let 12 be the adjacentr side (base) Let '5' be the opposite side ( perpendicular ) Let '13' by the hypotenuse. Sin(Angle) = opposite / hypotenuse = 5/13 Angle = Sin^(-1) 5/13 = 22.619... degrees. NB This is the angle between the hypotenuse and the base(adjacent) Now 'swopping' things around , we take the angle between the hypotenuse and the perpendicular (opposite) . This now becomes perpendicular(adjacent) and the base becomes the opposite. Hence Sin(angle) = 12/13 Angle = Sin^(-1) 12/13 = 67.380.... degrees. The angle at the 'top' of the triangle. Verification. ' 90 + 67.380... + 22.619... = 180 ( allow for calculator decimals).


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