How do you solve for the angles of this triangle with the following equations?

.enter image source here

The steps I used:
1. #sqrt(10^2+16^2+2*16*10*cos(110))#

  1. Cos(110)/c = Cos(A)/16

1 Answer
Jim G.
Apr 23, 2018

#"see explanation"#

Explanation:

#"using the formulae sine/cosine rules"#

#"we require to find side c"#

#"using the "color(blue)"cosine rule"#

#•color(white)(x)c^2=a^2+b^2-(2abcos110)#

#rArrc=sqrt(16^2+10^2-(2xx16xx10cos110)#

#color(white)(rArrc)=sqrt(256+100+109.445..)#

#color(white)(rArrc)~~21.57#

#"calculate "angleA" using the "color(blue)"sine rule"#

#•color(white)(x)a/(sinA)=b/(sinB)=c/(sinC)#

#rArr16/(sinA)=21.57/(sin110)#

#rArrsinA=(16xxsin110)/21.57#

#rArrangleA=sin^-1((16xxsin110)/21.57)~~44.2^@#

#"Find "angleB" using angle sum of triangle"#

#rArrangleB=180-(110+44.2)~~25.8^@#

Related questions
Impact of this question
395 views around the world
You can reuse this answer
Creative Commons License