A triangle with angles of A=38, B=83 and C=59. Side opposite to angle C is measuring 20. How do you find lengths of other sides?

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A triangle with angles of A=38, B=83 and C=59. Side opposite to angle C is measuring 20. How do you find lengths of other sides?

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Answer 1 · 2016-08-02T10:49:19

Use the Law of Sines to get
$a = 14.365, b = 23.151$ $a=14.365, b=23.151$

Explanation:

Given a triangle with angles $A, B, C$ $A, B, C$ and corresponding opposite side lengths $a, b, c$ $a, b, c$
Law of Sines:
$XXX \frac{a}{sin (A)} = \frac{b}{sin (B)} = \frac{c}{sin (C)}$ $color(white)("XXX")a/(sin(A))=b/(sin(B))=c/(sin(C))$

with the given data values
$XXX \frac{a}{sin (38^{\circ})} = \frac{b}{sin (83^{\circ})} = \frac{20}{sin (59^{\circ})}$ $color(white)("XXX")a/sin(38^@)=b/sin(83^@)=20/sin(59^@)$

$\Rightarrow$ $rArr$
$XXX a = sin (38^{\circ}) \cdot \frac{20}{sin (59^{\circ})} \approx 14.36502$ $color(white)("XXX")a=sin(38^@)*20/sin(59^@) ~~14.36502$
and
$XXX b = sin (83^{\circ}) \cdot \frac{20}{sin (59^{\circ})} \approx 23.15075$ $color(white)("XXX")b=sin(83^@)*20/sin(59^@)~~23.15075$

...The above is based on use of a calculator and the assumption that I didn't making typos in my data entry.

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A triangle with angles of A=38, B=83 and C=59. Side opposite to angle C is measuring 20. How do you find lengths of other sides?

1 Answer

Explanation:

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