Question

 If sin A = 3/4, Calculate cos A and tan A.​

Answer 1

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

• sin A = 3/4

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

• Value of cos A
• Value of tan A

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

Using Some Formula

$\star\tt{\blue{\:\sin\:A\:=\dfrac{(perpendicular)}{(Hypotenuse)}}}$

$\star\tt{\blue{\:\cos\:A\:=\:\dfrac{(Base)}{(Hypotenuse)}}}$

$\star\tt{\blue{\:\tan\:A\:=\:\dfrac{(Perpendicular)}{(Base)}}}$

$\star\tt{\blue{\:(Base)^2\:=\:(Hypotenuse)^2-(Perpendicular)^2}}$

Assume that, Here a right ∆PQR,

Where,

• PQ = Perpendicular = 3
• QR = Base
• RP = Hypotenuse = 4

Now, First calculate Base (QR)

So,

➥ (QR)² = (RP)² - (PQ)²

➥ QR² = 4² - 3²

➥ QR² = 16 - 9

➥ QR² = 7

➥ QR = √7

Since, Base (QR) be √7 .

Now, Calculate Cos A ,

➥ cos A = Base/Hypotenuse

Or,

➥ cos A = QR/RP

Keep Value of Base & Hypotenuse

➥ cos A = √7/4

Now, Calculate tan A

➥ tan A = Perpendicular/Base

➥ tan A = PQ/QR

Keep Value of Perpendicular & base

➥ tan A = 3/√7

$\Large{\underline{\underline{\mathfrak{\red{\bf{Hence}}}}}}$

• Value of cos A = √7/4
• Value of tan A = 3/√7

________________

Answer 2

$\underline{\underline{\blue{\textbf{Step - By - Step - Explanation : -}}}}$

To Find :

• We need to calculate the value of cas A and tan A

Solution :

• Sin A = 3/4

$\green{\textbf{sin A = Perpendicular/Hypotenuse}}$

• perpendicular = 3
• Hypotenuse = 4

By using Pythagoras theorem we have to find the value of base

Hypotenuse ² = base² + perpendicular ²

4² = b² + 3²

16 = b² + 9

b² = 16 - 9

b² = 7

b = √7

• Value of Cos A :-

$\green{\textbf{Cos A = Base/Hypotenuse}}$

Cos A = √7/4

• Value of tan A :-

$\green{\textbf{tan A = Perpendicular/Base}}$

tan A = 3/√7

$\large\dag \large { \blue{\underline{\bf{Hence }}}}$

$\red{\textrm{Value of cas A is √7/4 and tan A is 3/√7}}$

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