Question

if tan A = 3/4 and A is acute , then the value of cos A is​

Answer 1

Answer:

CosA= 4/5

Step-by-step explanation:

TanA = 3/4

TanA = perpendicular/ Base

So

from the Pythagoras Theorem be get the third side

if the sides of triangle are A , B and C where B 90°

then

Ac^2 = AB^2 + BC^2

Ac^2 = 3^2 + 4^2

= 9+16

= 25

AC = 5

Now Cos A = Base/Hypotence

Cos A = 4/5

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Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ \tan A = \frac{3}{4} \: \: \: and \: \:A \: is \: acute }$

TO DETERMINE

The value of cos A

EVALUATION

Here it is given that

$\displaystyle \sf{ \tan A = \frac{3}{4} }$

Now

$\displaystyle \sf{ {\tan}^{2} A = \frac{9}{16} }$

$\displaystyle \sf{ \implies \: 1 + {\tan}^{2} A = 1 + \frac{9}{16} }$

$\displaystyle \sf{ \implies \: {\sec}^{2} A = \frac{ 16 + 9}{16} }$

$\displaystyle \sf{ \implies \: {\sec}^{2} A = \frac{25}{16} }$

$\displaystyle \sf{ \implies \: {\sec}^{} A = \frac{5}{3} }$

$\displaystyle \sf{ \implies \: {\cos}^{} A = \frac{3}{5} }$

FINAL ANSWER

$\displaystyle \sf{ \: {\cos}^{} A = \frac{3}{5} }$

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