In circle SS, ST=5ST=5 and m\angle TSU=50^\circ∠TSU=50∘ Find the length of \overset{\LARGE\frown}{TU} TU⌢ . Express your answer as a fraction times \piπ.

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18-08-2022
Mathematics

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In circle SS, ST=5ST=5 and m\angle TSU=50^\circ∠TSU=50∘ Find the length of \overset{\LARGE\frown}{TU} TU⌢ . Express your answer as a fraction times \piπ.

$In circle SS ST5ST5 and mangle TSU50circTSU50 Find the length of oversetLARGEfrownTU TU Express your answer as a fraction times piπ class=$

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akposevictor akposevictor · Answer 1 · 2022-08-19T20:11:49+02:00

The length of arc TU, as a fraction terms of π, is calculated as: 25/18 π units.

How to Find the Length of an Arc of a Circle?

The length of an arc of a circle is the distance around the portion of the circumference of a circle that is marked by two points connected to the radius of the circle. Given r as the radius length and ∅ is the central angle measure, the length of the arc of the circle can be calculated as:

Arc length = ∅/360 × 2 × π × r.

Given the following:

Central angle (∅) = m∠TSU = 50°

Radius of the circle (r) = 5

Plug the values into ∅/360 × 2 × π × r:

Arc length = 50/360 × 2 × π × 5

Arc length = (50 × 2 × π × 5)/360

Arc length = 500/360 × π

Arc length = 50/36 × π

Arc length = 25/18 × π

Arc length of TU = 25/18 π units

Thus, the length of arc TU, as a fraction terms of π, is calculated as: 25/18 π units.

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