Suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120°. What is the length of the third side of the triangle?

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Answer 1 · 2016-09-29T05:09:11

#"The reqd. length="sqrt(3369)~~58.04.#

Let the Vertices of the #Delta" be "A,B, and C.#

We will follow the Usual Notation for #DeltaABC,# e.g., the side

opposite to the Vertex #A# will be denoted by #a, m/_A=A,# etc.

In this notation, let us assume that,

#a=32, b=35, &, C=120^@,.# & we have to find #c#.

Using Cosine-Rule for #DeltaABC#, we have,

#c^2=a^2+b^2-2abcosC#

#=32^2+35^2-2*32*35*cos120^@#

#=1024+ 1225-2240cos(180^@-60^@)#

#=2249-2240(-cos60^@)#

#=2249+2240(1/2)#

#=2249+1120#

#=3369#

#rArr c=sqrt(3369)~~58.04.#

Enjoy Maths.!