<span>The area of a triangle can be calculated by applying the law of sines </span> Area=(1/2)*a*b*sin C-----> sin C=2*A/[a*b]
Part a) <span>sides of length 5 cm and 8 cm, and area of 15 cm^2 a=5 cm b=8 cm A=15 cm</span>² sin C=2*A/[a*b]------> sin C=2*15/[5*8]----> sin C=3/4 C=arc sin (3/4)-----> C=48.59 degrees <span>the possible values of the included angle are </span>C1=48.59° C2=180°-48.59----> C2=131.41°
the answer Part a) is 48.59° and 131.41°
Part b) <span>sides of length 45 km and 53 km, and area 800 km^2 </span>a=45 km b=53 km A=800 km² sin C=2*A/[a*b]-----> sin C=2*800/[45*53]----> sin C=0.6709 C=arc sin (0.6709)-----> C=42.13° C1=42.13° C2=180-42.13°----> C2=137.87°