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

$θ = {12.536}^{o}$ $theta=12.536^o$

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

$\frac{1}{2} \times a \times b \times sin C$ $1/2xxaxxbxxsinC$

Hence in the given case, we have

$252 = \frac{1}{2} \times 27 \times 46 \times sin θ$ $252=1/2xx27xx46xxsintheta$ or

$sin θ = \frac{2 \times 252}{27 \times 46}$ $sintheta=(2xx252)/(27xx46)$

= $\frac{2 \times 9 \times 4 \times 7}{3 \times 9 \times 2 \times 43}$ $(2xx9xx4xx7)/(3xx9xx2xx43)$

= $\frac{4 \times 7}{3 \times 43} = \frac{28}{129} = 0.2171$ $(4xx7)/(3xx43)=28/129=0.2171$

Hence $θ = {12.536}^{o}$ $theta=12.536^o$