In a circle, if the length of an arc is 15 cm and the radius is 10 cm, what is t

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Question: In a circle, if the length of an arc is 15 cm and the radius is 10 cm, what is the angle in radians subtended by the arc at the center?

Options:

Correct Answer: 1.5 radians

Solution:

The angle θ in radians is given by the formula θ = arc length / radius. Therefore, θ = 15/10 = 1.5 radians.

In a circle, if the length of an arc is 15 cm and the radius is 10 cm, what is the angle in radians subtended by the arc at the center?

In a circle, if the length of an arc is 15 cm and the radius is 10 cm, what is the angle in radians subtended by the arc at the center?

Step 1: Identify the given values. The length of the arc is 15 cm and the radius of the circle is 10 cm.
Step 2: Write down the formula to find the angle in radians. The formula is θ = arc length / radius.
Step 3: Substitute the values into the formula. Replace 'arc length' with 15 cm and 'radius' with 10 cm.
Step 4: Calculate the angle. So, θ = 15 cm / 10 cm.
Step 5: Perform the division. 15 divided by 10 equals 1.5.
Step 6: Conclude that the angle subtended by the arc at the center is 1.5 radians.

Arc Length and Central Angle – Understanding the relationship between the length of an arc, the radius of the circle, and the angle subtended at the center.