Question

. If cosa = 4/5 and a is an acute angle, find the value of sina and tana​

Answer 1

Answer:

Sin(a) = 3/5 and Tan(a) = 3/4

Step-by-step explanation:

$cos \: (a) = \frac{4}{5}$

Cos(a) = Base / Hypotenuse

So, ( Taking x as the highest common factor ) ,

Base = 4x , Hypotenuse = 5x

By Pythagoras Theorem ,

${h}^{2} = {p}^{2} + {b}^{2}$

${(5x)}^{2} = {p}^{2} + {(4x)}^{2}$

${p}^{2} \: = 25 {x}^{2} - 16 {x}^{2} = 9 {x}^{2}$

${p}^{2} = {(3x)}^{2}$

$p \: = \: 3x$

So Perpendicular= 3x

Sin(a) = Perpendicular / Hypotenuse = 3x/5x = 3/5

Tan(a) = Perpendicular / Base = 3x/4x = 3/4

I hope this helps !