Question

if cos A is 1/2 then value of tan A ​

Answer 1

Answer:

The value of  $TanA = \sqrt{3}$.

Step-by-step explanation:

• Given,

  $CosA = \frac{1}{2}$

$CosA =\frac{Base}{Hypotenuse}= \frac{B}{H}$

we know that,

$TanA= \frac{Perpendicular }{Base} = \frac{P}{B}$

From Pythagoras Theorem, we know that

$H^{2} = P^{2} + B^{2}$

$2^{2} = 1^{2} + P^{2} \\4= 1+ P^{2}\\4-1=P^{2}\\P = \sqrt{3}$

So, we get

$TanA= \frac{P}{B} = \frac{\sqrt{3} }{1}$

Therefore, the value of $TanA = \sqrt{3}.$

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Answer 2

Answer:

The value of  tan A is $\sqrt{3}$.

Step-by-step explanation:

Step 1 of 2

It is given that the value of cos A is 1/2.

To find the value of tan A.

Consider the triangle PQR as follows:

As we know,

cos A = base/hypotenuse

         = QR/PR

Since cos A = 1/2

⇒ QR/PR = 1/2

⇒ QR = 1, PR = 2

Now,

In ΔPQR, by Pythagoras theorem,

$PR^2=QR^2+PQ^2$

$2^2=1^2+PQ^2$

$4=1+PQ^2$

$PQ^2=3$

$PQ=\sqrt{3}$

Thus, the length of PQ is $\sqrt{3}$.

Step 2 of 2

Find the value of tan A.

tan A = Perpendicular/base

         = PQ/QR

         = $\sqrt{3}/1$

         = $\sqrt{3}$

Final answer: The value of tan A is $\sqrt{3}$.

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