Question

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

.

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

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

Answer 1

`"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^@`