Question

In a triangle two sides are of length 20 and 21 and the sine of angle between them is equal to 0.6 then the third side is equal to

• A. $13or\sqrt{1513}$
• B. $14or\sqrt{1315}$
• C. $15or\sqrt{1531}$
• D. $17or\sqrt{1531}$

Answer 1

Answer: (A)

$13or\sqrt{1513}$

$\sin \theta =0.6$
$\cos \theta =0.8or-0.8$
$CaseI$
$0.8=\frac{{\left(20\right)}^2+{\left(21\right)}^2-b^2}{2\times 20\times 21}$....(using cos formula)
$b^2=169$
$4b=13$
$CaseII$
$-0.8=\frac{{\left(20\right)}^2+{\left(21\right)}^2-b^2}{2\times 20\times 21}$.....(using cos formula)
$b^2=1513$
$b=\sqrt{1513}$.