Solving a Trigonometric Equation to Hit a Moving Target

[peanut648]

So the orginial question asked what angle to fire a gun to hit a moving target, and i got all the way to 40sinθcosθ-10sinθ-1 = 0, but we aren't supposed to use calculators so how would you solve this by hand. Thanks!

 

[tiny-tim]

Welcome to PF!

Hi peanut648! Welcome to PF!

Either use cosθ = √(1 - sin²θ), or write everything in terms of tan(θ/2).