If cosec \(A = \frac{25}{7}\), then what is the value of Tan A?1. \(\

1.	If cosec \(A = \frac{25}{7}\), then what is the value of Tan A?1. \(\frac{7}{25}\)2. \(\frac{7}{24}\)3. \(\frac{25}{24}\)4. \(\frac{24}{25}\)
Answer» Correct Answer - Option 2 : \(\frac{7}{24}\) Given: Cosec A = 25/7 Formula Used: Cosec A = Hypotenuse/Perpendicular Tan A = Perpendicular/Base Calculation: Cosec A = Hypotenuse/Perpendicular = 25/7 From here we deduce that Hypotenuse = 25 Units and Perpendicular = 7 Units Using Pythagoras Theorem in right angle triangle ABC, where AB is perpendicular, BC is Base, and AC is Hypotenuse. AC² = AB² + BC² ⇒ (25)² = (7)²+ (BC)² ⇒ 625 = 49 + BC² ⇒ BC² = 625 -49 = 576 ⇒ BC = √576 = 24 Units (Base) Tan A = 7/24 ∴ The value of Tan A is 7/24

If cosec \(A = \frac{25}{7}\), then what is the value of Tan A?1. \(\frac{7}{25}\)2. \(\frac{7}{24}\)3. \(\frac{25}{24}\)4. \(\frac{24}{25}\)

Answer» Correct Answer - Option 2 : \(\frac{7}{24}\)

Given:

Cosec A = 25/7

Formula Used:

Cosec A = Hypotenuse/Perpendicular

Tan A = Perpendicular/Base

Calculation:

Cosec A = Hypotenuse/Perpendicular = 25/7

From here we deduce that Hypotenuse = 25 Units and Perpendicular = 7 Units

Using Pythagoras Theorem in right angle triangle ABC, where AB is perpendicular, BC is Base, and AC is Hypotenuse.

AC² = AB² + BC²

⇒ (25)² = (7)²+ (BC)²

⇒ 625 = 49 + BC²

⇒ BC² = 625 -49 = 576

⇒ BC = √576 = 24 Units (Base)

Tan A = 7/24

∴ The value of Tan A is 7/24