How do you find remaining sides and angles of triangle given side a =4, side b = 1, angle y = 100?

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Answer 1 · 2018-02-26T14:51:26

$color(red)(c = 4.2883, hatA = 66.7^@, hat B = 13.3^@$

$hat C = 100^@, b = 1, a = 4$

To find $c, hatA, hat B$

Applying law of Cosines,

enter image source here
$c = sqrt (a^2 + b^2 - (2 a b cos C))$

$c = sqrt(4^2 + 1^2 - (2 * 4 * 1 * cos 100)) = 4.2883$

Applying law of sines, enter image source here

$hat A = sin ^-1 ((a sin C) / c) = sin ^-1 ((4 * sin 100) / 4.2883 )= 66.7^@$

$hat B = 180 - 100 - 66.7 = 13.3^@$