How do you solve the triangle when given 3, 4, and 6?

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Answer 1 · 2018-04-02T06:26:59

$color(blue)("Area of " Delta ~~) color(crimson)( 5.94 " sq units"$

$a = 3, b = 4, c = 6$

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

$cos C = (c^2 - a^2 - b^2) / (2 * a * b)$

$cos c = (6^2 - 3^2 - 4^2) / (2 * 3 * 4) = 0.1382$

$hat C = cos ^-1 (0.1382) = 1.4322^c$

$"Area of " Delta = (1/2) a b sin C$

$=> (1/2) * 3 * 4 * sin (1.4322) ~~ 5.94 " sq units"$