What is the arc length if θ = 7 pi over 4 and the radius is 5?

Mathematics

2 answers:

PolarNik [594]2 years ago

4 0

The formula for arc length is:

s= r∅

Given that ∅= 7π/4

and r= 5

Therefore, arc length s= 7π/4 *5 = 35π/4

jarptica [38.1K]2 years ago

4 0

Answer: The required arc length will be 27.5 units.

Step-by-step explanation: We are given to find the arc length with the following information :

$\theta=\dfrac{7\pi}{4},~~~\textup{radius},~r=5.$

We know that the length of an arc with angle subtended at the center α and radius of the circle r units is given by

$\ell=r\alpha.$

Therefore, the required arc length will be

$\ell=r\theta=5\times\dfrac{7\pi}{4}=\dfrac{35}{4}\times \dfrac{22}{7}=\dfrac{5\times 11}{2}=\dfrac{55}{2}=27.5.$

Thus, the required arc length will be 27.5 units.

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