How do you find the exact value of the third side given #triangle PQR#, p=6, #q=sqrt2# and #mangleR=pi/4#?

1 Answer
Dec 23, 2016

Answer:

#r=sqrt26=5.1#

Explanation:

We can find the value of third side if two sides and measure of included angle between them is given. We use Law of cosines for this, according to which if two sides #p# and #q# and included angle #R# are given, then

#r^2=p^2+q^2-2pq cosR#

Here, we are given #p=6#, #q=sqrt2# and #R=pi/4#

Hence, #r^2=6^2+(sqrt2)^2-2xx6xxsqrt2xxcos(pi/4)#

= #36+2-12xxsqrt2xx1/sqrt2=38-12=26#

Hence #r=sqrt26=5.1#