Which of the following trigonometric ratios are correctly written in context of ABCas given?

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Solution

Q.
Which of the following trigonometric ratios are correctly written in context of $∆ A B C a s g i v e n$

$(i) s i n A = \frac{B C}{A C} (i i) t a n C = \frac{B C}{A B} (i i i) c o s C = \frac{A B}{A C} (i v) s e c A = \frac{A C}{A B}$

1 (i) and (ii)

2 (ii) and (iv)

3 (i) and (iv)

4 (ii) and (iii)

Ans.
(3)

$W h e n ∠ A i s u n d e r c o n s i d e r a t i o n B a s e = A B, P e r p e n d i c u l a r = B C, H y p o t e n u s e = A C ∴ s i n A = \frac{Perpendicular}{Hypotenuse} = \frac{B C}{A C} and s e c A = \frac{Hypotenuse}{Base} = \frac{A C}{A B} W h e n ∠ C i s u n d e r c o n s i d e r a t i o n : B a s e = B C, P e r p e n d i c u l a r = A B, H y p o t e n u s e = A C ∴ t a n C = \frac{Perpendicular}{Base} = \frac{A B}{B C} and c o s C = \frac{Base}{Hypotenuse} = \frac{B C}{A C}$

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