How do you find the exact value of the third side given triangle ABC, b=4, c=4, and $m ∠ A = \frac{π}{3}$ $mangleA=pi/3$ ?

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Answer 1 · 2017-02-07T06:25:41

Applying the Cosine Rule , $a^{2} = b^{2} + c^{2} - 2 b c cos A$ $a^2=b^2+c^2-2bc cosA$

$= 16 + 16 - 2 (4) (4) cos (\frac{π}{3}) = 16 + 16 - 2 (4) (4) (\frac{1}{2})$ $=16+16-2(4)(4)cos(pi/3)=16+16-2(4)(4)(1/2)$

$= 16 + 16 - 16 = 16$ $=16+16-16=16$ .

$:. a=4$ .

Alternatively , in $DeltaABC, b=c rArr m/_B=m/_C, &, m/_A=pi/3$

$rArr m/_B=m/_C=m/_A=pi/3 rArr Delta ABC is" equilateral."$

$:.a=b=c=4.$

How do you find the exact value of the third side given triangle ABC, b=4, c=4, and mangleA=pi/3m∠A=π3mangleA=pi/3?