1 pt Consider the triangle below not drawn to scale Let a 5

(1 pt) Consider the triangle below (not drawn to scale) Let a = 5, b = 7 and = 1 10°. Find the length of side c and measure of the angles, LA and LB (in degrees). Give your answer to at least 3 decimal places. c= LA=

Solution

1)a=5,b=7,C=110^o

by law of cosines

c²=a²+b²-2abcosC

c²=5²+7²-2*5*7cos110^o

c=9.897

by law of sines a/sinA=b/sinB=c/sinC

a/sinA=c/sinC

5/sinA=9.897/sin110⁰

sinA=(5/9.897)sin110⁰

A=28.342^o

7/sinB=9.897/sin110⁰

sinB=(7/9.897)sin110⁰

B=41.654^o