Question

if tanA=3/4,find all other t-ratios
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Answer 1

$\bf\large\blue{Question\::-}$

• $\bf{If\:tan\:A = \frac{3}{4},\: find \: all \: other \: trigonometrical\:ratios\:.}$

$\bf\large\blue{Solution\::-}$

$\star$ We know, tan = $\frac{height}{base}$

therefore, height = 3

and, base. = 4

>> Now, by applying Pythagoras Theorem we can find out the value of hypotenuse.

hypotenuse ² = height ² + base ²

$\implies \: hypotenuse \: ^{2} = {3}^{2} + {4}^{2}$

$\implies \: hypotenuse \: ^{2} = 9 + 16$

$\implies \: hypotenuse \: ^{2} = 25$

$\implies \: hypotenuse = \sqrt{25}$

$\implies \: hypotenuse = 5$

Now we have the values of hypotenuse, height and base .

So we can find all the six trigonometrical ratios .

$\bf\large\blue{Answer\::-}$

$\bf{sin\: A = \frac{height}{hypotenuse} = \frac{3}{5}}$

$\bf{cos\: A = \frac{base}{hypotenuse} = \frac{4}{5}}$

$\bf{tan\: A = \frac{height}{base} = \frac{3}{4}}$

$\bf{cot\: A = \frac{base}{height} = \frac{4}{3}}$

$\bf{cosec\: A = \frac{hypotenuse}{base} = \frac{5}{4}}$

$\bf{sec\: A = \frac{hypotenuse}{height} = \frac{5}{3}}$

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$\bf\large\blue{Hope\:it\:helps\:you\:.}$