Question 1121733: In ABC, A=45 degrees, b=15 cm and c=22 cm. Find the area of the triangle. Found 2 solutions by Boreal, ikleyn:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Find a by Law of Cosines:
a^2=b^2+c^2-2bc cos A
a^2=225+484-2(330) cos 45
=709-660(0.7071)=709-466.69=242.31
sqrt(242.31)=15.6 (rounded)
length of all 3 sides combined is 52.6 and half of it, 26.3, is s
sqrt(s*(s-a)(s-b)(s-c))=sqrt(26.3*11.3*4.3*10.7)=sqrt (13673.71)
=116.9 cm^2 (Hero's Formula)
In this problem, two side lengths of the triangle are given and the angle concluded between these two sides.
Then the area of the triangle is equal to
A = = = 116.67 cm^2.
