How do you find the measurement of the included angle θ between two sides of a triangle if the two side measurements are 27m and 46m and the area of the triangle is 252 square meters?

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Answer 1 · 2016-07-04T08:36:29

#theta=12.536^o#

Area of a triangle, when two sides and included angle are given, is give by

#1/2xxaxxbxxsinC#

Hence in the given case, we have

#252=1/2xx27xx46xxsintheta# or

#sintheta=(2xx252)/(27xx46)#

= #(2xx9xx4xx7)/(3xx9xx2xx43)#

= #(4xx7)/(3xx43)=28/129=0.2171#

Hence #theta=12.536^o#