Question

Question #55c8f

Answer 1

`cos(a) = 5/13 " OR " -5/13`

Explanation:

`"Use the very well known identity "sin^2(x) + cos^2(x) = 1.`
`=> (12/13)^2 + cos^2(x) = 1`
`=> cos^2(x) = 1 - (12/13)^2`
`=> cos^2(x) = 1 - 144/169 = 25/169`
`=> cos(x) = pm 5/13`

Answer 2

`cos a = 5/13`

Explanation:

From basic right-angled trigonometry we can deduce the following.

`sin a = 12/13` means that the length of the opposite side is `12` and the length of the hypotenuse is `13`

Use Pythagoras' Theorem to find the length of the adjacent side,

`a^2 = 13^2-12^2 = 25`

`a = sqrt25 = 5`

You might also have recognised the Pythagorean Triple: `5,12,13`

Now that you know the length of the adjacent side you can determine the value of `cos a`

`cos a = a/h = 5/13`