Question

यदि tanA=3/4 तो cosA=?​

Answer 1

Given: tanA = $\frac{3}{4}$

To Find: cosA

Solution:

We know that in a right angled triangle:

Hypotenuse: It is the largest side of the triangle. Also, it is opposite the right angle of the triangle.

Base: The side on which the right angle triangle stands is known as its base. Moreover, any of the two sides other than the hypotenuse can be chosen as the base for performing the calculation.

Perpendicular: It is the side perpendicular to the base of the right-angled triangle and it is opposite to $\theta$.

Let's understand this with the attached figure:

We know that tan$\theta$ = $\frac{Perpendicular}{Base}$

Therefore, we can say that $\frac{Perpendicular}{Base} = \frac{3}{4}$

So, from above, we can also say that:

Perpendicular = $3$

Base = $4$

• Firstly, we will calculate hypotenuse by using the Pythagorean Theorem which states:
• $(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2}$

• By putting Perpendicular = $3$ and Base = $4$ units, we get:

$(Hypotenuse)^{2} = (4)^{2} + (3)^{2}$

• By squaring 4 and 3, we get:

$(Hypotenuse)^{2} = 16 + 9$

• Add the following:

$(Hypotenuse)^{2} = 25$

• Take the square symbol to the other side and hence, make it root.

$Hypotenuse = \sqrt{25}$

• Now doing the square root of $25$.

$Hypotenuse = 5$

• Since we have got the hypotenuse, we will now calculate cosA by using the trigonometric rule which is stated below:

$cos\theta = \frac{Base}{Hypotenuse}$

• Now, by putting Base = $4$ and Hypotenuse = $5$, we get:

$cosA = \frac{4}{5}$

Final Answer:

Hence, the value of cosA is $\frac{4}{5}$.