A triangle has sides A, B, and C. Sides A and B are of lengths 9 and 8, respectively, and the angle between A and B is pi/4. What is the length of side C?

1 Answer
Tony B
Jan 7, 2016

C = sqrt(82)

Explanation:

Note that pi/4" radians "-> 45^o

Tony_BTony_B

Let /_cdb = pi/2 " that is: " 90^o

As/_ dcb = pi/4 " then " /_cbd=pi/4

Thus it follows that bd =dc=9

Thus ad = 9-8=1

By Pythagoras: (bd)^2+(da)^2 = C^2

=> C = sqrt( (bd)^2+(da)^2)

=> C = sqrt(9^2+1^2) =sqrt(82)

Whilst 82 is not prime it is a product of prime numbers. As far as I am aware the only way of showing the precise value of C is to express it in this form.

Thus C = sqrt(82)

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