Question

if tan A =4/3,then sin A and cos A find

Answer 1

$given \: \tan(a) = \frac{4}{3} \\ \\ we \: know \\ \\ \tan(a) = \frac{p}{b} \\ \\ where \: p = 4 \\ \\ and \: \\ \\ b = 3 \\ \\ now \: we \: know \\ \\ by \: using \: pgt \\ \\ we \: get \\ \\ {p}^{2} + {b}^{2} = {h}^{2} \\ \\ {4}^{2} + {3}^{2} = 16 + 9 = 25 \\ \\ h = 5 \\ \\ sin(a) = \frac{p}{h} = \frac{4}{5} \\ \\ and \\ \\ \cos(a) = \frac{b}{h} = \frac{3}{5} \\ \\ hope \: this \: helps \: you$
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Answer 2

Given: tan A =4/3

To find: The value of sin A and cos A.

Solution:

The tangent of an acute angle is calculated by dividing the perpendicular by the base of a right-angled triangle. According to the question, the tangent of the acute angle of the right-angled triangle is 4/3. Hence, the perpendicular is 4 units and the base is 3 units. Now, the hypotenuse of the triangle can be calculated using the Pythagoras Theorem as follows.

$hyp = \sqrt{4^{2} + 3^{2} }$

      $= 5 units$

Now, the sine and cosine of an acute angle of a right-angled triangle can be written as follows.

$sin A = \frac{perpendicular}{hypotenuse}$

        $= \frac{4}{5}$

$cos A = \frac{base}{hypotenuse}$

        $= \frac{3}{5}$

Therefore, the value of sin A and cos A is 4/5 and 3/5, respectively.