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Some Applications Of Trigonometry

Question
CBSEENMA10007930

In ΔABC right angled at A, given ∠B = 30°, AC = 3 cm. Find AB, BC and ∠ACB.

Solution
Given: ∠B = 30°, ∠A = 90° and AC = 3 cm

 In increment ABC comma
     angle straight A plus angle straight B plus angle straight C space equals space 180 degree
rightwards double arrow space space space 90 degree plus 30 degree plus angle straight C space equals space 180 degree
rightwards double arrow space space space space 120 degree space plus space angle straight C space equals space 180 degree
rightwards double arrow space space space space space space space space space space space space space space space space space space angle straight C space equals space 60 degree
Now,    space space tan space 30 degree space equals space AC over AB
rightwards double arrow         fraction numerator 1 over denominator square root of 3 end fraction equals 3 over AB
rightwards double arrow           AB space equals space 3 square root of 3 space cm
and sin space 30 degree space equals space AC over BC
rightwards double arrow space space space space space space space space space space space 1 half space equals space 3 over BC
rightwards double arrow space space space space space space space space space space space BC space equals space 6 space cm
space Hence comma space space space space space angle straight C space equals space 60 degree comma space space AB space equals space 3 square root of 3 space cm comma
and space space space space space space space space space space space space space BC space equals space 6 space cm.

Some More Questions From Some Applications of Trigonometry Chapter

In ΔABC, right angled at B. AB = 24 cm, BC = 7 cm. Determine:
(i) sin A cos A,
(ii) sin C, cos C.