Two sides of a triangle are 4 centimetres and 6 centimetres and the angle between the two sides is 50 - Maths - Trigonometry

Question

Two sides of a triangle are 4 centimetres and 6 centimetres and the
angle between the two sides is 50 degree Find the length of the
third side of the triangle

Priyanka Kedia · Accepted Answer

Dear Student,

Given, two sides of a triangle are 4cm and 6 cm and the angle between the two side is 500
Using law of cosines, c2=a2+b2-2abcosC⇒c2=42+62-2×4×6 cos500⇒c2=16+36-48 cos500⇒c2=52-48 cos500⇒c2=52-48×0
643    cos 500=0 6427≈0
643⇒c2=52-30 86400⇒c2=21 13600⇒c=4
597⇒c≈4
6 cmHence, the third side of the triangle is 4
6 cm

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Two sides of a triangle are 4 centimetres and 6 centimetres and the angle between the two sides is 50 degree. Find the length of the third side of the triangle.