The length of missing sides a = 5 units and b = 5/2 units.
What is Trigonometric ratios?
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In ΔABC,
AB (Base) = [tex]\frac{5\sqrt{3}}{2}[/tex] , BC(Hypotenuse) = a , CA (perpendicular) = b
and ∠ABC = [tex]30^0[/tex]
Now,
tan [tex]30^0[/tex] = perp. / base
tan [tex]30^0[/tex] = b /[tex]\frac{5\sqrt{3}}{2}[/tex] = 2b/[tex]5\sqrt{3}[/tex]
[tex]\frac{1}{\sqrt{3} } = \frac{2b}{5\sqrt{3} }[/tex]
[tex]2b = 5[/tex]
b = 5/2
Similarly, sin [tex]30^0[/tex] = perp. / Hypo.
[tex]sin 30^0 = CA / BC[/tex]
[tex]\frac{1}{2} = \frac{b}{a}[/tex]
a = 2b
a = 2 X 5/2
a = 5.
Thus, the length of missing sides a = 5 units and b = 5/2 units
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