Question

10. If sinA = 3/4 calculate cosA and tanA​

Answer 1

Given:-

• Sin A = 3/4

To find:-

• Values of cos A and tan A

Solution:-

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

$\longmapsto\boxed{\displaystyle{\frac{Opposite}{Hypotenuse} \ = \ \frac{3}{4}}}$

$\Longrightarrow\displaystyle{\frac{BC}{AC} \ = \ \frac{3}{4}}$

Let,

BC = 3x

AC = 4x

We find AB using Pythagoras Theorem

Hence, Using Pythagoras Theorem

(Hypotenuse)² = (Height)² + (Base)²

$\Longrightarrow$ AC² = AB² + BC²

$\Longrightarrow$ (4x)² = AB² + (3x)²

$\Longrightarrow$ 16x² = AB² + 9x²

$\Longrightarrow$ 16x² - 9x² = AB²

$\Longrightarrow$ 7x² = AB²

$\Longrightarrow$ AB² = 7x²

$\Longrightarrow$ AB = √7x²

$\Longrightarrow$ AB = √7x

Now, we need to find cos A & tan A

$\longmapsto\boxed{\displaystyle{cos A \ = \ \frac{adjacent}{Hypotenuse}}}$

$\Longrightarrow\displaystyle{\frac{AB}{AC}}$

$\Longrightarrow\displaystyle{\frac{\sqrt{7x}}{4x}}}$

$\Longrightarrow\bf{\frac{\sqrt{7}}{4}}$

$\longmapsto\boxed{\displaystyle{tan A \ = \ \frac{opposite}{adjacent}}}$

$\Longrightarrow\displaystyle{\frac{BC}{AB}}$

$\Longrightarrow\displaystyle{\frac{3x}{\sqrt{7x}}$

$\Longrightarrow\bf{\frac{3}{\sqrt{7}}}$

Therefore, the values of cos A = √7/4 and tan A = 3/√7.