show that the trigonometric ratio of an acute angle in right triangle Express the relationship between the angle and the length of its sides
Answers
Solution :-
In right angled ∆ABC right angle at C we have angle A and angle B are acute angles . { Acute angles < 90° . }
Let,
- AC = b unit
- BC = a unit
- AB = Hypotenuse = c unit .
So, Trigonometric ratios for acute ∠A :-
→ sin A = Perpendicular/Hypotenuse = a/c
→ cos A = Base/Hypotenuse = b/c
→ tan A = Perpendicular/Base = a/b
→ cosec A = Hypotenuse/Perpendicular = c/a
→ sec A = Hypotenuse/Base = c/b
→ cot A = Base/Perpendicular = b/a
and, Trigonometric ratios for acute ∠B :-
→ sin B = Perpendicular/Hypotenuse = b/c
→ cos B = Base/Hypotenuse = a/c
→ tan B = Perpendicular/Base = b/a
→ cosec B = Hypotenuse/Perpendicular = c/b
→ sec B = Hypotenuse/Base = c/a
→ cot B = Base/Perpendicular = a/b
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