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What angle is subtended by an arc 1.70 m in length on the circumference of a circle with a radius of 2.70 m?

Answer :

Final answer:

The angle subtended by an arc on the circumference of a circle, measured in radians, is calculated by dividing the arc length by the radius. Substitute the given arc length (1.70 m) and radius (2.70 m) into the formula Δθ = A/r to find the answer.

Explanation:

In order to find the angle subtended by an arc on the circumference of a circle, we need to use the relationship between arc length, radius and angle in radians. In mathematics, the quantity Δθ = A/r is defined as the ratio of the arc length (A) to the radius (r) of curvature of a circular path, where Δθ is measured in units of radians.

In this question, you're given the arc length A as 1.70 m and the radius of curvature as 2.70 m:

  • Calculate Δθ = A/r
  • Substitute the given values: Δθ = 1.70 m / 2.70 m
  • Perform the division to find the value of Δθ, which will give the angle subtended by the arc in radians.

Remember to keep the final answer in radians, as it is the standard unit of angular measure in mathematics, and does not require conversion.

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