Solve the triangle with sides a=2,c=4, angle x=30 degrees. state the law that you use?

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Answer 1 · 2018-02-26T09:08:17

$ˆ B = 60^{\circ}, b = 2 \sqrt{3}, ˆ C = 90^{\circ}$ $color(blue)(hat B = 60^@, b = 2sqrt3, hat C = 90^@$

$a = 2, c = 4, ˆ C = 30^{\circ}$ $a = 2, c = 4, hat C = 30^@$

Applying law of sines,
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$ˆ C = {sin}^{- 1} (\frac{sin 30 \cdot 4}{2}) = {sin}^{- 1} 1 = 90^{\circ}$ $hat C = sin ^-1 ((sin 30 * 4) / 2) = sin^-1 1 = 90^@$

enter image source here

It’s a right triangle with angles measuring $30, 60, 90$ $30, 60, 90$

Hence sides will be in the ratio $x : \sqrt{3} x : 2 x$ $x : sqrt3 x : 2x$

Hence $ˆ B = 60^{\circ}, b = 2 \sqrt{3}, ˆ C = 90^{\circ}$ $hat B = 60^@, b = 2sqrt3, hat C = 90^@$