The circle below has center K, and its radius is 7yd. Given that =m∠LKM70°, find the length of the minor arc LM.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.LMK70°LengthofminorarcLM:
Question
The circle below has center K, and its radius is 7yd. Given that =m∠LKM70°, find the length of the minor arc LM.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.LMK70°LengthofminorarcLM:
Solution
To find the length of the minor arc LM, we need to use the formula for the length of an arc, which is:
Arc length = (central angle/360) * 2πr
where:
- the central angle is the measure of ∠LKM, which is 70°,
- r is the radius of the circle, which is 7yd.
Substituting these values into the formula, we get:
Arc length = (70/360) * 2π * 7
Simplify the fraction 70/360 to 7/36 and multiply it by 2π * 7:
Arc length = (7/36) * 2π * 7
Arc length = (7/18) * π * 7
Arc length = 49/18 π yd
So, the length of the minor arc LM is 49/18 π yards.
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