Question

7. Given tan A = 5/12 , find the other trigonometric ratios of the angle A. *

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Answer 1

Answer:

Step-by-step explanation:

tan A = 5/12 = Opposite side/ adjacent side 

Assume a right angled triangle.  Find the hypotenuse using the pythagoras theorem. Hypotenuse = √(144+25) = √169 = 13

Sin A = Opposite side / Hypotenuse = 5/13 

Cos A  = Adjacent side / Hypotenuse  = 12/13

Cot A = 1/tan A =12/5

Cosec A = 1/sin A =13/5

sec A = 1/ cos A = 13/12  

Answer 2

To Find :

• we need to find the other Trignometric ratios of Angle A.

Given :

• Tan A = 5/12

Solution :

we know that,

• Tan A = perpendicular/base

So,

• Perpendicular = 5
• Base = 12

By using Pythagoras theorem :-

⇛Hypotenuse ² = base² + perpendicular ²

⇛H² = 12² + 5²

⇛H² = 144 + 25

⇛H² = 169

⇛H = √169

⇛H = 13

• Cot A = Base/perpendicular

⟹ Cot A = 12/5

• Sin A = perpendicular/Hypotenuse

⟹ Sin A = 5/13

• Cosec A = Hypotenuse/perpendicular

⟹ Cosec A = 13/5

• Cos A = Base/hypotenuse

⟹ Cos A = 12/13

• Sec A = Hypotenuse/Base

⟹ Sec A = 13/12

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