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

Answers

Answer 1
Answer:

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 = √(22.0528)

  = 4.6960

c = 4.70 cm

Thus |AB| = 4.70 cm

ii. Applying the sine rule;

(a)/(sin A) = (b)/(sin B) = (c)/(sin C)

(4.12)/(Sin A) = (4.7)/(sin 42.5)

sin A = (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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