Why Tan 45 Degrees Equals One
An animated explainer showing why the tangent of 45 degrees always equals 1. Starting with a small right triangle where opposite and adjacent sides are equal, the triangle is scaled up repeatedly to show the ratio never changes. The formula tan θ = opposite/adjacent is revealed after the visual pattern, followed by a real-world example calculating a tower's height using a 45° angle of elevation. Useful for Grade 9-10 students learning basic trigonometric ratios.
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The prompt that made it
Create a visually engaging 90-second animated explainer for Grade 9–10 students on one idea in trigonometry: Why does tan 45° = 1? Start with a simple 45° right triangle where opposite = 2 and adjacent = 2. Show that opposite/adjacent = 1. Then enlarge the triangle to opposite = 4 and adjacent = 4, and then 8 and 8. Visually demonstrate that although the triangle gets bigger, the ratio always remains 1. Reveal only after this visual discovery: tan θ = opposite / adjacent Therefore: tan 45° = 1 End with a simple real-world example: a person stands 20 m from a tower and sees the top at a 45° angle. Show visually why the tower is 20 m tall. Keep the animation simple, intuitive, modern and visual, with minimal text and conversational narration. Prioritize animated triangles, highlighting, scaling and equation transformations over lengthy explanations. Do not explain sine, cosine or SOH-CAH-TOA.
Make the next one in this series
- Show why tan 30° and tan 60° give different fixed ratios using scaled triangles
- Explain angle of elevation and depression with animated real-world tower and ship examples
- Visually demonstrate how tan θ changes as the angle increases from 0° to 90°
