Question

if sinC=15/17,then find cosC? Using trigonometric identity

Answer 1

sinC = 15 / 17


$\bold{ \: we \: know \: \sin(a) = \frac{height}{hypotenuse} }$


So,


$\frac{height}{hypotenuse} = \frac{15}{17}$


Now, Let height = 15 x and hypotenuse = 17x





Using Pythagoras Theorem,

Base = √ { ( 17x )² - ( 15x )² }

base = √ { 289x² - 225x² }

base = √64 x²

Base = 8x





$\mathbf{we \: know \: \: \: \cos(a) = \frac{base}{hypotenuse} }$


Due to which,


cosC = 8x / 17x

cosC = 8 / 17

Answer 2

Heya !!

Sin C = 15/17

Using trigonometric identity ,

Sin² theta + Cos² theta = 1





Cos² theta = (1 - Sin² theta)

sin C = 15/17

Cos² C = ( 1 - Sin² C )

Cos² C= 1 - (15/17)²

Cos² C = 1 - 225 / 289

Cos² C = 289 - 225 / 289

Cos² C = 64/289

Cos C = root 64 / root 289

Cos C = 8/17