Question

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

Answer 1

Answer :

$\sf cosA = \dfrac{\sqrt{7}}{4}$

$\sf tanA = \dfrac{3}{\sqrt{7}}$

Solution :

We know that,

$\sf sin \theta = \dfrac{Perpendicular}{Hypotenuse}$

According to Statement,

$\sf sin \theta = \dfrac{3}{4}$

$\sf \implies \dfrac{Perpendicular}{Hypotenuse} = \dfrac{3}{4}$

∴ Perpendicular for θ = 3x

and the hypotenuse for θ = 4x

By Pythagoras' Theorem,

Hypotenuse² = Perpendicular² + Base²

$\sf⇒ AC² = AB² + BC²$

$\sf⇒ (4x)² = (3x)² + BC²$

$\sf⇒ 16x² = 9x² + BC²$

$\sf⇒ 16x² - 9x² = BC²$

$\sf⇒ 7x² = BC²$

$\sf⇒ \sqrt{7x^{2}} = BC$

$\sf⇒ BC = \sqrt{7}x$

Now, We have cosA and tanA will be,

$\sf cosA = \dfrac{Base}{Hypotenuse}$

$\sf⇒ cosA = \dfrac{\sqrt{7}x}{4x}$

$\sf⇒ cosA = \dfrac{\sqrt{7}}{4}$

$\sf tanA = \dfrac{Perpendicular}{Base}$

$\sf⇒ tanA = \dfrac{3x}{\sqrt{7}x}$

$\sf⇒ tanA = \dfrac{3}{\sqrt{7}}$