Question

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, if-sin-a-3-4-calculate-cos-a-and-tan-a

Answer 2

$\huge\tt\colorbox{blue}{\color{orange}{Answer}}$

$\huge{\underline{\underline{Given}}}$

$sin \: A = \frac{3}{4}$

$\huge{\underline{\underline{To\: find:-}}}$

$cos \: A \: \: and \: tan \: A$

$\huge{\underline{\underline{Proof:-}}}$

We know that

${cos}^{2} A = 1 - \sin^{2} A$

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${cos}^{2} A = 1 - \frac{3}{4} \times</p><p> \frac{3}{4}$

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${cos}^{2} A = 1 - \frac{9}{16}$

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${cos}^{2} A = \frac{16 - 9}{16}$

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${cos}^{2} A = \frac{7}{16}$

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$cos \: A = \sqrt{\frac{7}{16} }$

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$cos \: A = \frac{ \sqrt{7} }{4}$

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${ \tan} \: A = \frac{ \sin \: A}{ \cos \: A}$

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$tan \: A = \frac{3}{4} \times \frac{4}{\sqrt{7} }$

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$tan \: A = \frac{3}{ \sqrt{7} }$