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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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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).
When a man walks 5m towards east and turns right and moves 12m the magnitude of his displacement is 13m how?
Pythagoras. The right turn is assumed to be 90 degrees, and moving southwards. This forms the two shorter sides on a right angled triangle. They applying Pythagoras. h^)2) = 5^(2) + 12^(2) h^(2) = 25 + 144 h^(2) = 169 Don't forget to 'square root' both sides!!!! Hence h = sqrt(169) = 13 . This is a classic Pythagorean triangle.
The foot of a ladder is placed 5 feet from a building the top of the ladder rests 12 feet up on the building how long is the ladder?
13 feet
2 cards are drawn at random from a pack of 52 cards. find the probability that both the cards are spades?
P(First card) = 13/52 P(second card = 12/51 Because you have already drawn one spade , there is one less card in the pack . P(Both spades) = 13/52 X 12/51 = 156/2652 = 0.0588
Find the reciprocal of the complex number 3 plus 2i Give your answer in the usual a plus bi form?
It is 3/13 - 2/13*i
