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📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 \tan 45^\circ = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1

📌 Geometrically, in a right triangle with angles \(45^\circ\), the legs are equal (isosceles right triangle), so \(\tan 45^\circ = \frac{\text{opposite}}{\text{adjacent}} = 1\). Thus, \(\tan 45^\circ = \boxed{1}\).

📌 A right triangle has legs measuring 8 cm and 15 cm. Find the radius of the circle inscribed in the triangle.

📌 First, compute the hypotenuse \(c\) using the Pythagorean theorem:

📌 c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \text{ cm}

📌 A = \frac{1}{2} \times 8 \times 15 = 60 \text{ square cm}

📌 s = \frac{8 + 15 + 17}{2} = 20 \text{ cm}

📌 r = \frac{A}{s} = \frac{60}{20} = 3 \text{ cm}

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