Solve each triangles for the unknown side lengths and angle

Solve each triangles for the unknown side lengths and angle measures Find the area of each polygon. Show the formulas used. Obtuse triangle Regular octagon trapezoid

Solution

10)by law of sines a_/sinA=b_/sinB=c_/sinC

a_/sinA=c_/sinC

17_/sinA=26_/sin90^o

sinA =(17_/26)sin90^o

sinA =(17_/26)*1

A=40.83^o

A+B+C=180^o

40.83^o+B+90^o=180^o

B=49.17^o

b_/sinB=c_/sinC

b_/sin49.17^o=26_/sin90^o

b=26sin49.17^o_/sin90^o

b=19.67

==========================================

11)by law of cosines c²=a²+b²-2abcosC

c²=25²+19²-2*25*19cos100^o

c=33.93

by law of sines a_/sinA=b_/sinB=c_/sinC

a_/sinA=c_/sinC

_25/sinA=33.93_/sin100^o

sinA=(25_/33.93)*sin100^o

A=46.53^o

A+B+C=180^o

46.53^o+B+100^o=180^o

B=33.47^o