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
Jan 7, 2016

Answer:

C = #sqrt(82)#

Explanation:

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

Tony_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)#