Find the possible values of the included angle of a triangle with: A) sides of length 5 cm and 8 cm, and area of 15 cm^2B) sides of length 45 km and 53 km, and area 800 km^2.
Accepted Solution
A:
we know that
The area of a triangle can be calculated by applying the law of sines
Area=(1/2)*a*b*sin C-----> sin C=2*A/[a*b]
Part a) sides of length 5 cm and 8 cm, and area of 15 cm^2 a=5 cm b=8 cm A=15 cm² 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 the possible values of the included angle are C1=48.59° C2=180°-48.59----> C2=131.41°
the answer Part a) is 48.59° and 131.41°
Part b) sides of length 45 km and 53 km, and area 800 km^2 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°