Question

Find the indicated trigonometric ratio as a fraction in simplest form. (Hint: You need to find the missing side of the triangle before you do anything.)

Answer 1

The indicated trigonometric ratio as a fraction in simplest form is:

sin L = 3 / 5 = 0.6

tan N = 4 / 3 = 1.33

cos L = 4 / 5 = 0.8

sin N = 4 / 5 = 0.8

By using pythagoreas theorem

(hypotenuse)²= (base)² +
`(perpendicular) ^2`

(LN)²= (MN)² +
`(LM)^2`

(10)²= (6)² + (LM)²

100 = 36 +
`(LM)^2`

`(LM)^2`= 100-36

`(LM)^2` = 64

(LM) = √64

The square root of 64 is 8

so,

LM = 8

The required trigonometric ratio are

1. sin = opposite / hypotenuse

sin L = MN / NL

= 6 / 10

= 3 / 5

= 0.6

2.. tan = opposite / adajcent

tan N = ML / MN

= 8 / 6

= 4 / 3

= 1.33

3. cos = adjacent / hypotenuse

cos L = ML / NL

= 8 / 10

= 4 / 5

= 0.8

4. sin = opposite / hypotenuse

sin N = ML / NL

= 8 / 10

= 4 / 5

= 0.8