Question

In a circle with aradius 8.9 an angle intercepts an arc of length 15.9 find the angle in radians to the nearest 10th ?

Answer 1

Main Answer:

The measure of the central angle, formed in a circle with a radius of 8.9 units and intercepting an arc of length 15.9 units, is approximately 1.8 radians to the nearest tenth.

Step-by-step explanation:

In a circle, the relationship between the central angle
`(\( \theta \))`, the radius
`(\( r \))`, and the arc length
`(\( s \))` is given by the formula
`\( s = r \theta \)`.

Given that the radius
`(\( r \))` is 8.9 and the arc length
`(\( s \))` is 15.9, we can rearrange the formula to solve for the central angle
`(\( \theta \)): \( \theta = (s)/(r) \)`.

Plugging in the values,
`\( \theta = (15.9)/(8.9) \approx 1.8 \)` radians (rounded to the nearest tenth).

Therefore, the central angle, in radians, intercepting an arc of length 15.9 in a circle with a radius of 8.9, is approximately 1.8 radians to the nearest tenth.