Show the need for trigonometry with questions like: How can you calculate the width of a river that you can't cross.
Then develop the actual motivation for sin, cos, tan (important note: historically, the first trigonometric function was the chord function)
Then discover that if you had a table of trigonometric values you could easily do these kinds of measurements like the one we started with, so you need to discover what sin(a+b) and sin(a/2) are.