A triangle has sides A, B, and C. Sides A and B are of lengths #14# and #12#, respectively, and the angle between A and B is #(5pi)/8 #. What is the length of side C?

1 Answer
Mar 10, 2016

Answer:

≈ 21.647 units

Explanation:

Given a triangle with 2 sides and the angle between them known, find the 3rd side using the #color(blue)" cosine rule "#

# c^2 = a^2 + b^2 - (2ab costheta)#

where c is the side to be found , a and b are the known sides and #theta " is the angle between them "#

here a = 14 , b = 12 and #theta = (5pi)/8#

hence #c^2 = 14^2 + 12^2 -( 2xx14xx12 cos((5pi)/8))#

# = 196+144 + 128.582...# ≈ 468.582

#rArr c = sqrt468.582 ≈ 21.647 " units " #