Question

in a triangle ABC ,if A+B=90',cotB=3/4,then find the value of cos A

Answer 1

This should be your answer.

Answer 2

Answer:

$\frac{4}{5}$

Step-by-step explanation:

Given :In a triangle ABC ,if A+B=90°

          $Cot B = \frac{3}{4}$

To Find : Find the value of cos A

Solution:

ΔABC

∠A+∠B+∠C= 180° (Angle sum property of triangle )  ---1

We are given that A+B=90°

Substitute the value in 1

90°+∠C= 180°

∠C= 180°-90°

∠C= 90°

So, ΔABC is a right angled triangle at C

$Cot \theta = \frac{Base}{Perpendicular}$

We are given that  $Cot B = \frac{3}{4}$

So, On comparing

For ∠B

Base = 3

Perpendicular =4

Now to find Hypotenuse we will use Pythagoras theorem

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

$Hypotenuse^2=4^2+3^2$

$Hypotenuse^2=16+9$

$Hypotenuse^2=25$

$Hypotenuse=\sqrt{25}$

$Hypotenuse=5$

Now For ∠A

Base = 4

Perpendicular = 3

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

$Cos A = \frac{4}{5}$

Hence  the value of cos A is $\frac{4}{5}$