How do you solve the triangle given A=25, B=78, a=13.7?

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How do you solve the triangle given A=25, B=78, a=13.7?

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Answer 1 · 2017-01-05T13:12:01

$(∠ A, ∠ B, ∠ C) = (25^{\circ}, 78^{\circ}, 77^{\circ})$ $(/_A,/_B,/_C) = (25^@,78^@,77^@)$
$(a, b, c) = (13.7, 31.71, 31.59)$ $(a,b,c)=(13.7,31.71,31.59)$
$XXX$ $color(white)("XXX")$ ( $b$ $b$ and $c$ $c$ are approximate)

Explanation:

If $∠ A = 25^{\circ}$ $/_A=25^@$
and $∠ B = 78^{\circ}$ $/_B=78^@$
then
$XXX ∠ C = 180^{\circ} - (25^{\circ} + 78^{\circ}) = 77^{\circ}$ $color(white)("XXX")/_C=180^@-(25^@+78^@)=77^@$

Given $a = 13.7$ $a=13.7$ and using the Law of Sines
$XXX b = \frac{a}{sin (∠ A)} \cdot sin (∠ B) \approx 31.7085733$ $color(white)("XXX")b=a/(sin(/_A))*sin(/_B) ~~31.7085733$
and
$XXX c = \frac{a}{sin (∠ A)} \cdot sin (∠ C) \approx 31.58611706$ $color(white)("XXX")c=a/(sin(/_A)) * sin(/_C) ~~31.58611706$

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How do you solve the triangle given A=25, B=78, a=13.7?

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