How do you find the area of #triangle PQR# given #p=212#, #q=287#, #mangleR=124^@#?

1 Answer
Douglas K.
Apr 19, 2018

We can choose either side to compute the height of the triangle; I shall choose #p#:

#"Height" = p sin(R)#

Substitute #p = 212# and #R = 124^@#:

#"Height" = 212 sin(124^@)#

#"Height" ~~ 175.8#

The area of the triangle is:

#"Area" = 1/2"Base" xx "Height"#

By choosing #p# for the computation of the height, we have forced the choice of the base to be #q#. Substitute #"Base = 287"# and #"Height" ~~ 175.8#:

#"Area" = 1/2 287 xx 175.8#

#"Area" = 25227.3#

I will leave it to you to show that you obtain the same area if you choose #q# to compute the height and #p# to the base.

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