How do you solve the triangle ABC, given a=10, A=35, B=25?

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Answer 1 · 2018-02-25T13:29:11

Solution : $b = 7.3681, c = 15.0987, ˆ C = 120^{\circ}$ $color(red)(b = 7.3681, c = 15.0987, hatC = 120^@$

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Given 2a = 10, hat A = 35, hat B = 25#

$ˆ C = 180 - 35 - 25 = 120$ $hatC = 180 - 35 - 25 = color(red)(120$

Applying Law of Sines,

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $color(green)(a/sin A = b / sin B = c / sin C$

$b = \frac{a sin B}{sin A} = \frac{10 \cdot sin 25}{sin 35} = 7.3681$ $b = (a sin B) / sin A = (10 * sin 25) / sin 35 = color(red)(7.3681$

$c = \frac{a sin C}{sin A} = \frac{10 sin 120}{sin 35} = 15.0987$ $c = (a sin C) / sin A = (10 sin 120) / sin 35 = color(red)(15.0987$