Question

The lengths if side AB and side BC of a scalene triangle ABC are 12cm and 8 cm respectively. The size of angle C is 59 degrees. Find the length of side AC.

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Answer 1

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We have been given angle C = 59° ≈ 60°

(cos 59° and cos 60° differs by 0.01 so I take a practical value of cos 59° ≈ 0.5 )

So by cosine rule :

cos 60° = [(BC)²+(AC)²-(AB)²]/(2×BC×AC)

1/2 =[(8)² + (AC)²-(12)²]/(2× 8×AC)

8× AC = (AC)² - 80

0 = (AC)² -8(AC) -80

AC = [+8±√(64+320)]/2 (By quadratic formula)

AC = (8±18)/2

But AC being a side can't be negative

Hence AC must be (8+18)/2

i.e AC = 13 cm

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