Question

25
Given 15 cot A =8, find sin A and sec A.​

Answer 1

Step-by-step explanation:

cot A=8/15 = AC/EC

BY applying pythagorus theorm

AE^2=AC^2+EC^2

(8)^2+(15)^2=AE^2

64+225=AE^2

289=AE^2

AE=17

Sin A=EC/AE= 15/17

Sec A=AE/AC= 17/8

Answer 2

• Sin A = 15/7
• Sec A = 17/8

Step-by-step explanation:

To find:-

• Value of sin A and sec A.

Solution:-

Given that,

15 cot A = 8

Cot A = 8/15

Cot θ = Base/Perpendicular

Cot A = 8/15

Base = 8 and Perpendicular = 15

Sin θ = Perpendicular/Hypotenuse

• We do not have Hypotenuse for sin θ.

By Pythagoras theorem

(Hypotenuse)² + (Base)² + (Perpendicular)²

➔ Hypotenuse² = (8)² + (15)²

➔ Hypotenuse² = 64 + 225

➔ Hypotenuse² = 289

➔ Hypotenuse = √289

➔ Hypotenuse = 17

So, Hypotenuse is 17

Sin A :-

Sin θ = Perpendicular/Hypotenuse

Sin A = 15/17

Sec A :-

Sec θ = Hypotenuse/Base

Sec A = 17/8

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More ratio's :-

• Tan θ = Perpendicular/Base
• Cosec θ = Hypotenuse/Perpendicular
• Cos θ = Base/Perpendicular