Question

if sin A =3/4 , calculate cos A and tan A... ​

Answer 1

Answer:

The value of cos A is 5/4 and value of tan A is 3/5

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Answer 2

Given:

• Sin A = ¾

To Find:

• Calculate Cos A and tan A.

Solution:

Let assume a right angled ∆ABC, right angled at B

$\\ {\underbrace{\tt\large{ Understanding \ the \ Concept }}}$

Sin function is the equal to the ratio of length of the opposite side to the hypotenuse side.

$\bigstar{\underline{\boxed{\tt\green{ Sin \ A = \dfrac{Opposite \ side}{Hypotenuse} }}}}$

$\implies$ ${\tt{ \dfrac{3}{4} }}$

Let BC be 3k and AC will be 4k

where as

• k = Positive real number.

$\\ {\underbrace{\tt\large\purple{Concept \ Used }}}$

According to the Pythagoras theorem, the squares of the hypotenuse side is equal to the sum of the squares of the other two sides of a right angle triangle.

AC² = AB² + BC²

Substitute the value of AC and BC

$\implies$ (4k)² = AB² + (3k)²

$\implies$ 16k² − 9k² = AB²

$\implies$ AB² = 7k²

Therefore, AB = √7k

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Now,

• Find the value of cos A and tan A

$\\ \bigstar{\underline{\boxed{\sf{ Cos \ (A) = \dfrac{Adjacent \ side}{Hypotenuse} }}}}$

Substituting the value of AB and AC;

After Cancel the constant k in both numerator and denominator;

$\implies$ AB/AC = √7k/4k

$\implies$ √7/4

Therefore,

• Cos (A) = √7/4

$\\ \bigstar{\underline{\boxed{\sf\red{ tan \ (A) = \dfrac{Opposite \ side}{Adjacent \ side} }}}}$

Substituting the Value of BC and AB;

After Cancel the constant k in both numerator and denominator;

$\implies$ BC/AB = 3k/√7k

$\implies$ 3/√7

Therefore,

• Tan A = 3/√7