Question

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

Answer 1

Answer:

Let, Side opposite to angle θ = BC =3k and Hypotenuse = AC =4k

where, k is any positive integer So, by Pythagoras theorem,

we can find the third side of a triangle

⇒ (AB)2 + (BC)2 = (AC)2

⇒ (AB)2 + (3k)2 = (4k)2

⇒ (AB)2 + 9k2 = 16k2

⇒ (AB)2 = 16 k2 – 9 k2

⇒ (AB)2 = 7 k2

⇒ AB =k√7

So, AB = k√7

Now, we have to find the value of cos A and tan A We know that,

The side opposite to angle A = BC =3k

The side adjacent to angle A = AB =k√7

Step-by-step explanation:

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Answer 2

Required Answer:-

Given:

• sin(A) = 3/4

To find:

• cos(A) and,
• tan(A)

Solution:

We know that,

➡ sin²(x) + cos²(x) = 1

Here,

➡ sin(A) = 3/4

➡ (3/4)² + cos²(A) = 1

➡ cos²(A) = 1 - 9/16

➡ cos²(A) = (16 - 9)/16

➡ cos²(A) = 7/16

➡ cos(A) = √(7/16)

➡ cos(A) = √7/4 — (i)

We also know that,

➡ tan(A) = sin(A)/cos(A)

➡ tan(A) = 3/4 ÷ √7/4

➡ tan(A) = 3/4 × 4/√7

➡ tan(A) = 3/√7

Hence,

➡ cos(A) = √7/4

➡ tan(A) = 3/√7

Answer:

• cos(A) = √7/4
• tan(A) = 3/√7