Question 1029643
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The area of ΔPQR is 18.  If p = 6 and q = 8, find all of the possible measures of ∠R
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The area of a triangle is equal half the product of the dimensions of its two sides by the sine of the angle between them:

S = {{{(1/2)*p*q*sin(alpha))}}}.

In other words,

18 = {{{(1/2)*6*8*sin(alpha)}}},   or

18 = {{{24*sin(alpha)}}},   or

{{{sin(alpha)}}} = {{{18/24}}} = {{{3/4}}}.

There are two solutions for {{{alpha}}}:

1) {{{alpha}}} = {{{arcsin(3/4)}}} = 0.848 rad = 48.6°  (acute angle),  and/or

2) {{{alpha}}} = 180 - 48.6 = 131.4° (obtuse angle). 
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