What is the value of tan 45°?

## The reasoning The tangent of an angle is the ratio: **tan θ = opposite/adjacent** (or sin θ/cos θ). For the special angle 45°, picture an **isosceles right triangle** where both legs are equal. Let's say both legs = 1 unit. tan 45° = opposite/adjacent = 1/1 = **1** You can also remember: sin 45° = cos 45° = √2/2, so tan 45° = (√2/2)/(√2/2) = 1. **Key principle:** In a 45-45-90 triangle, the two legs are always equal, making their ratio exactly 1. ## Why the wrong options tempt you **A) 0** — This is tan 0°, not tan 45°. Students confuse small angles. **B) 1/2** — Some guess this looks "reasonable" or confuse it with sin 30° (which is 1/2). **D) √3** — This is tan 60°! It's easy to mix up the special angles 30°, 45°, and 60°. ## Quick takeaway **45° gives you equality**: tan 45° = 1 because you're dividing equal sides. Memorize: tan 30° = 1/√3, tan 45° = 1, tan 60° = √3.