Measure of the third side of a given triangle is approximately equals to
[tex]49.5mm[/tex] .
" Triangle is defined as the two dimensional geometric shape with three sides , three vertices and three angles enclosed in it."
Formula used
Cosine law of a triangle,
[tex]c^{2} =a^{2} + b^{2} -2ab cos\theta[/tex]
[tex]a, b, c[/tex] are sides opposite to [tex]\angle A,\angle B, \angle C[/tex] respectively.
[tex]1cm =10mm[/tex]
According to the question,
As per diagram drawn for the given conditions of triangle we have,
[tex]a = 6cm\\\\b = 8cm\\\\\angle \theta = 47[/tex]°
Substitute the values in the cosine law of triangle we get,
[tex]c^{2} =6^{2} +8^{2} -2 \times 6\times 8 \times cos47\\\\\implies c^{2} = 36 + 64 - 96 (0.682)\\\\\implies c^{2} = 100 - 65.472\\\\\implies c^{2} = 24.528[/tex]
[tex]\implies c = \sqrt{24.528}\\ \\\implies c = 4.95cm[/tex]
Therefore , [tex]c= 49.5mm[/tex] nearest millimeter.
Hence, measure of the third side of a given triangle is approximately equals to [tex]49.5mm[/tex] .
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