Given a triangleABC with a=10, b=20 and /_C=95^circ, what are the lengths of all sides and size of all angles?

1 Answer
Alan P.
Sep 21, 2016

{: (a,color(white)("XX"),b,color(white)("XX"),c,color(white)("XX"),/_A,color(white)("XX"),/_B,color(white)("XX"),/_C), (10,color(white)("XX"),20,color(white)("XX"),23.1,color(white)("XX"),25.5^@,color(white)("XX"),59.5^@,color(white)("XX"),95^@) :}

Explanation:

Use the Law of Cosines and the Law of Sines:
enter image source here

Given
color(white)("XXX")a=10, b=20, /_C=95^@

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A calculator/spreadsheet will be used for all calculations beyond this point and all final values should be taken as accurate to 1 decimal digit).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

By the Law of Cosines:
color(white)("XXX")c=sqrt(10^2+20^2-2(1)(20)(cos(95^@)))

color(white)("XXXX")=23.1

By the Law of Sines
color(white)("XXX")sin(A)=(sin(95^@)xx10)/23.1=0.430748

color(white)("XXX")A = "arcsin"(sin(A))="arcsin"(0.430748)=25.5^@

Similarly
color(white)("XXX")sin(B)=(sin(95^@)xx20)/(23.1)=0.861496

color(white)("XXX")B="arcsin"(sin(B))="arcsin"(0.861496)=59.5^@

Related questions
See all questions in Vector Operations
Impact of this question
1968 views around the world
You can reuse this answer
Creative Commons License