Answer:
Part 1) [tex]\angle\ C=50.3\°[/tex]
Part 2) [tex]\angle\ B=67.4\°[/tex]
Part 3) [tex]\angle\ A=62.3\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle C
Applying the law of cosines
[tex]c^{2} =a^{2} +b^{2} -2(a)(b)cos(C)[/tex]
substitute the given values and solve for cos(C)
[tex]20^{2} =23^{2} +24^{2} -2(23)(24)cos(C)[/tex]
[tex]2(23)(24)cos(C)=23^{2} +24^{2} -20^{2}[/tex]
[tex]1,104cos(C)=705[/tex]
[tex]cos(C)=705/1,104[/tex]
[tex]C=arccos(705/1,104)=50.3\°[/tex]
step 2
Find the measure of angle B
Applying the law of cosines
[tex]b^{2} =c^{2} +a^{2} -2(c)(a)cos(B)[/tex]
substitute the given values and solve for cos(B)
[tex]24^{2} =20^{2} +23^{2} -2(20)(23)cos(B)[/tex]
[tex]2(20)(23)cos(B)=20^{2} +23^{2} -24^{2}[/tex]
[tex]920cos(B)=353[/tex]
[tex]cos(B)=353/920[/tex]
[tex]B=arccos(353/920)=67.4\°[/tex]
step 3
Find the measure of angle A
Remember that the sum of the internal angles of triangle must be equal to 180 degrees
[tex]\angle\ A+\angle\ B+\angle\ C=180\°[/tex]
substitute the given values and solve for ∠A
[tex]\angle\ A+67.4\°+50.3\°=180\°[/tex]
[tex]\angle\ A=180\°-117.7\°[/tex]
[tex]\angle\ A=62.3\°[/tex]
