In fig abcd is a rectangle with dc=8cm and bc=6cm line segment cm is drawn making an angle 30degree with dc interacting ad in m find the lengths of cm and dm.
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Solution :-
In ∆MDC we have,
→ ∠MDC = 90° { Each angle of a rectangle is equal to 90°. }
→ DC = 8 cm { given. }
→ ∠ DCM = 30° { given. }
so,
→ tan 30° = Perpendicular / Base
→ tan 30° = DM / DC
→ 1/√3 = DM/8
→ DM = (8/√3) * (√3/√3)
→ DM = (8√3/3) cm (Ans.)
and,
→ cos 30° = Base / Hypotenuse .
→ cos 30° = DC / CM
→ √3/2 = 8/CM
→ CM = (16/√3) * (√3/√3)
→ CM = (16√3/3) cm (Ans.)
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