Introduction To Trignometry

NCERT Chapter Solutions

Question: In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine :
(i) sin A, cos A
(ii) sin C, cos C
Answer: In ΔABC, a rt angled Δ, by applying Pythagoras theorem
$AC^2 = AB^2 + BC^2$
 $\Rightarrow = (24)^2 + (7)^2$
 $\Rightarrow = 576 + 49$
 $\Rightarrow = 625$
$AC = \sqrt{625} = 25 cm$

i. $ sin A = \frac{\text {side opposite ∠A}}{hypotenuse} = \frac{BC}{AC} = \frac{7}{25}$

  $ cos A = \frac{\text{side adjacent to ∠A }}{hypotenuse} = \frac {AB}{AC} = \frac{24}{25}$

ii. $ sin C = \frac{\text {side opposite ∠C}}{hypotenuse} = \frac{AB}{AC} = \frac{24}{25}$

  $ cos C = \frac{\text{side adjacent to ∠C }}{hypotenuse} = \frac {BC}{AC} = \frac{7}{25}$

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