Answer:
Part 1) [tex]m\angle A=58.41^o[/tex]
Part 2) [tex]m\angle B=73.40^o[/tex]
Part 3) [tex]m\angle C=48.19^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle A
we know that
Applying the law of cosines
[tex]BC^2=AB^2+AC^2-2(AB)(AC)cos(A)[/tex]
substitute the given values
[tex]8^2=7^2+9^2-2(7)(9)cos(A)[/tex]
[tex]64=130-126cos(A)[/tex]
[tex]126cos(A)=130-64[/tex]
[tex]126cos(A)=66[/tex]
[tex]cos(A)=66/126[/tex]
using calculator
[tex]m\angle A=cos^{-1}(66/126)= 58.41^o[/tex]
step 2
Find the measure of angle B
we know that
Applying the law of cosines
[tex]AC^2=AB^2+BC^2-2(AB)(BC)cos(B)[/tex]
substitute the given values
[tex]9^2=7^2+8^2-2(7)(8)cos(B)[/tex]
[tex]81=113-112cos(B)[/tex]
[tex]112cos(B)=113-81[/tex]
[tex]112cos(B)=32[/tex]
[tex]cos(B)=32/112[/tex]
using calculator
[tex]m\angle B=cos^{-1}(32/112)= 73.40^o[/tex]
step 3
Find the measure of angle C
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]A+B+C=180^o[/tex]
substitute the given values
[tex]58.41^o+73.40^o+C=180^o[/tex]
[tex]131.81^o+C=180^o[/tex]
[tex]C=180^o-131.81^o=48.19^o[/tex]
