Question

Use the Pythagorean identity

to find cos X.
15
19
?]√
sin x =
COS X =

Answer 1

Explanation:

So sin is defined as
`(opposite)/(hypotenuse)`. and cosine is defined as
`(adjacent)/(hypoteunse)`. So we need the adjacent side. Since we already have the opposite, and hypotenuse, you can use the Pythagorean identity to solve for the missing side:
`a^2+b^2 = c^2`

`15^2 + b^2 = 19^2`

`225 + b^2 = 361`

`b^2 = 136`

`b = √(136)`

`b = √(4) * √(34)`

`b = 2√(34)`

This is the adjacent side, so now plug this into the cosine equation and you get:
`(2√(34))/(19)`