Complementary Angles (Equal Range)
Shows that two launch angles that sum to 90° — for example 30° and 60° — produce identical horizontal range
The equation
What it solves
Shows that two launch angles that sum to 90° — for example 30° and 60° — produce identical horizontal range. The identity sin(2θ) = sin(π − 2θ) is the algebraic reason.
When to use it
Projectile range problems where the question asks for a second angle that achieves the same range, or to check that two given angles are range-equivalent.
When NOT to use it
Only valid for level ground (same launch and landing height) with no air resistance. With drag, the symmetry breaks and the two angles no longer give equal ranges.
Common mistakes
Confusing complementary (sum = 90°) with supplementary (sum = 180°). Applying the identity to peak height — complementary angles do not give equal peak heights. Forgetting that the 45° angle is its own complement and gives maximum range.