Question

Prove that $tan 45° = 1$ geometrically.

Approach

Consider an isosceles right triangle ABC with $∠ A = ∠ C = 45°$ and $∠ B = 90°$ . Let AB = BC = x. Then $tan 45° = \frac{A B}{BC} = \frac{x}{x} = 1$ .

Step-by-step working

1
Consider isosceles right triangle with equal sides; correct figure and angle sum property
1 mark
2
$tan 45° = \frac{opposite}{adjacent} = \frac{x}{x} = 1$
1 mark

Concepts used

trigonometric ratiosgeometric proofisosceles right triangle

Approach

Step-by-step working

Concepts used

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