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nalin [4]
3 years ago
13

For a circle with a diameter

Mathematics
1 answer:
meriva3 years ago
6 0

Answer:

The measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°

Step-by-step explanation:

Here, the diameter of the circle = 6 m

Diameter = 2 x RADIUS

So, radius  = D / 2  = 6 / 2  = 3 m

Also, the length of the arc = ( \frac{5}{2}  \pi) meters

Putting π  = 3.14, we get  

The length S of the arc = \frac{5}{2}  \times (3.14)  =  7.85  

or, S  = 7.85 m

Let us assume the arc subtends angle Ф at the center of the circle.

⇒  S  = r Ф

or, Ф = \frac{S}{r}   = \frac{7.85}{3}  =  2.61

⇒Ф  = 2.61 radians

Now, 1 Radian  = 57.2958 Degrees

⇒ 2. 62 Radian  = 2.61  x  ( 57.2958 Degrees)  =  149.542 °

or, Ф    =  149.542°

Hence, the measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°

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