Question

show that the trigonometric ratio of an acute angle in right triangle Express the relationship between the angle and the length of its sides ​

Answer 1

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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