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kotegsom [21]
3 years ago
15

in triangle abc |BC|=4.12cm ,|AC|=6.82cm and angle BCA is 42.5 . Calculate|AB| . and angle bac and angle abc​

History
1 answer:
PtichkaEL [24]3 years ago
8 0

Answer:

i. |AB| = 4.70 cm

ii. BAC = 36.3^{o}

iii. ABC = 101.2^{o}

Explanation:

i Let |AB| be represented by c, |AC| by b and |BC| by a. Since the question would give an included angle triangle, we first apply cosine rule.

c^{2} = a^{2} + b^{2} - 2ab Cos C

   = (4.12)^{2} + (6.82)^{2} - 2(4.12*6.82) Cos 42.5^{o}

   = 16.9744 + 46.5124 - 56.1968*0.7373

   = 63.4868 - 41.4340

c^{2} = 22.0528

c = \sqrt{22.0528}

  = 4.6960

c = 4.70 cm

Thus |AB| = 4.70 cm

ii. Applying the sine rule;

\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}

\frac{4.12}{Sin A} = \frac{4.7}{sin 42.5}

sin A = \frac{4.12*sin 42.5}{4.7}

         = 0.5922

A = sin^{-1} 0.5922

   = 36.3

BAC = 36.3^{o}

But,

iii. BCA + BAC + ABC = 180^{o}

42.5^{o} + 36.3^{o} + ABC = 180^{o}

ABC = 180^{o} - 78.8

       = 101.2

ABC = 101.2^{o}

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