Question

Give each trigonometric ratio as a fraction in simplest form. Need help ASAP!

Answer 1

`Sin \ L = (15)/(17)\\\\Cos \ L = (8)/(17)\\\\Tan \ L = (15)/(8)\\\\\\Sin \ M = (8)/(17)\\\\Cos \ M = (15)/(17)\\\\Tan \ M =(8)/(15)`

Explanation:

Trigonometric ratio:

First find the unknown side using Pythagorean theorem.

KM² = ML² - KL²

= 34² - 16²

= 1156 - 256

= 900

KM = √900

KM = 30

`Sin \ L = (Opposite \ side \ of \ L)/(hypotenuse)\\\\\\`

`= (KM)/(LM)\\\\\\=(30)/(34)=(15)/(17)`

`Cos \ L = (adjacent \ side \ of \ L )/(hypotenuse)\\\\`

`=(KL)/(LM)\\\\=(16)/(34)\\\\= (8)/(17)`

`Tan \ L = (opposite \ side \ of \ L)/(adjacent \ side \ of \ L)`

`= (KM)/(KL)\\\\=(30)/(16)\\\\=(15)/(8)`

`Sin \ M = (Opposite \ side \ of \ M)/(hypotenuse)\\\\\\`

`=(KL)/(LM)\\\\=(16)/(34)\\\\= (8)/(17)`

`Cos \ M = (adjacent \ side \ of \ M )/(hypotenuse)\\\\`

`= (KM)/(LM)\\\\\\=(30)/(34)=(15)/(17)`

`Tan \ M = (opposite \ side \ of \ M)/(adjacent \ side \ of \ M)`

`= (KL)/(KM)\\\\\\=(16)/(30)\\\\=(8)/(15)`