Question

Prove that $tan 4 5^{\circ} = 1$ geometrically.

Approach

In a $4 5^{\circ} - 4 5^{\circ} - 9 0^{\circ}$ triangle, the two legs are equal. If each leg is 1, then $tan 4 5^{\circ} = \frac{opposite}{adjacent} = \frac{1}{1} = 1$ .

Step-by-step working

1
Draw a $4 5^{\circ} - 4 5^{\circ} - 9 0^{\circ}$ triangle with legs = 1
0.5 marks
2
$tan 4 5^{\circ} = \frac{1}{1} = 1$
1.5 marks

Concepts used

tan45 degreesgeometric proofisosceles right triangle

Approach

Step-by-step working

Concepts used

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