Question

Using a right triangle, (picture provided below) find an algebraic expression for cos(theta)

Answer 1

What is the definition of cos(theta) in terms of opposite, adjacent, hypotenuse?

Answer 2

it's adj/hyp right?

Answer 3

@aum

Answer 4

correct. cos(theta) = adj / hyp = ? / x
We know the hypotenuse which is given as "x" in the diagram.
We know the opposite but we don't know the adjacent.
So we have to find the adjacent.
Use Pythagoras theorem

Answer 5

AB^2 + BC^2 = AC^2
AB^2 = AC^2 - BC^2 = x^2 - 2
AB = sqrt(x^2 - 2)

cos(theta) = adjacent / hypotenuse = \(\Large \frac{\sqrt{x^2-2}}{x} \)

Answer 6

that makes so much sense now! I can't thank you enough :)