A triangle has sides A, B, and C. Sides A and B are of lengths #11# and #12#, respectively, and the angle between A and B is #(5pi)/8 #. What is the length of side C?

1 Answer
Apr 12, 2016

Answer:

≈ 19.13

Explanation:

In a triangle , given 2 sides and the angle between them, to find the 3rd side use the #color(blue)" cosine rule "#

#color(red)(|bar(ul(color(white)(a/a)color(black)( c^2 = a^2 + b^2 - (2abcosC))color(white)(a/a)|)))#

where a , b are the 2 known sides and angle C , is the angle between them.
here a = 11 , b = 12 and angle C = #(5pi)/8#

substituting these values into the formula

# c^2 = 11^2 + 12^2 - ( 2xx11xx12xxcos((5pi)/8) )#

# = 121 + 144 - ( -101.03) = 366.03#

now # c^2 = 366.03 rArr c = sqrt366.03 ≈ 19.13 #