The missing side 'a' of the triangle ABC is 96.80 units.
What is a triangle?
A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
Let ABC be the triangle and a,b,c be the respective sides of the triangle.
The diagram below shows that the triangle with their dimensions.
The dimensions are
A=60°, b=50, c=48.
The two sides and one angle of the triangle are given.
The missing side a can be found by using the law of cosines,
[tex]a=\sqrt{b^{2}+c^{2} -2abcosA }[/tex]
Substitute the above values,
⇒ [tex]a=\sqrt{50^{2}+48^{2} -2(50)(48)cos60 }[/tex]
⇒ [tex]a=\sqrt{2500+2304-4800(-0.9524)}[/tex]
⇒ [tex]a=\sqrt{2500+2304+4571.58}[/tex]
⇒ [tex]a=\sqrt{9375.58}[/tex]
⇒ [tex]a=96.82[/tex] ≈ [tex]96.80[/tex]
Hence we can conclude that the missing side 'a' of the triangle ABC is 96.80 units.
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