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Home » LCM includes $2^2$, $3$, $5$, $7$, $13$, $109$ - Dachbleche24

LCM includes $2^2$, $3$, $5$, $7$, $13$, $109$ - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 C = 2\pi r = 2\pi \times 2.5 = 5\pi \text{ cm}

📌 Thus, the circumference of the circle is \(\boxed{5\pi}\) cm.

📌 Compute \(\tan 45^\circ\) using the unit circle and confirm its geometric interpretation.

📌 On the unit circle, the angle \(45^\circ\) corresponds to the point \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\). The tangent of an angle is the ratio of the y-coordinate to the x-coordinate:

📌 \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:

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