Question

if cos A=12 by 13 find the value of cot A​

Answer 1

If cos A=12 by 13 then the value of cot A​ is $\frac{13}{25}$

Solution:

Given that,

$\cos A=\frac{12}{13}$  ---- eqn 1

To find: The value of cot A

$\cos \theta=\frac{\text { base }}{\text { hypotenuse }}$  ----- eqn 2

By comparing eqn 1 and eqn 2 we get,

Thus base = 12 and hypotenuse = 13

By Pythagoras theorem, we get

$\begin{array}{l}{\text { Hypotenuse }^{2}=\text { perpendicular }^{2}+\text { base }^{2}} \\\\ {\text { perpendicular }^{2}=\text { Hypotenuse }^{2}-\text { base }^{2}}\end{array}$

$\begin{array}{l}{=13^{2}-12^{2}} \\\\ {=169-144} \\\\ {=25}\end{array}$

Thus perpendicular = 25

Now we have to find the value of cot A

$\cot A=\frac{\text { base }}{\text { Perpendicular }}$

Plugging in values we get,

$\cot A=\frac{13}{25}$

Thus the value of cot A is found

Learn more about trignometry

If cosA=12/13, then find Sina and tanA

https://brainly.in/question/980924

If cos A=12/13 then tan A

https://brainly.in/question/3122357

Answer 2

cotA= 12/5

Step-by-step explanation:

We know that,

In a right angle triangle ABC,where A is a right angle,

$cos A=Base/Hypotenuse$

cosA=12/13

On applying Pythagoras theorem in ΔABC,

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$

$(13)^2=(Perpendicular)^2+(12)^2$

$169=(Perpendicular)^2+144$

$(Perpendicular)^2=169-144$

                             =25

On taking Square root,

Perpendicular= 5

Now,

cotA= Base/Perpendicular

       =12/5