A 30o angle cuts off an arc in a circle with a diameter of 10 in. Find the length of the arc to the nearest hundredth.

You did not ask the right question. \
1. How to adjust the distance sprinkled?
2 Hot to adjust the arc of the sprinkler on adjustable arcs.
.......
1. distance ... there is a small screw on the flapper. screw it in to hit more water to spray a lesser distance.
2. there are two wires under the adjustable arc. Move them.

circumference is pye times twice the radius or by the diameter
3.1417 X 6 ( diameter or 2 times the radius )= 18.8496
90 degrees is 1/4 of the circumference
18.8496 divided by 4 = 4.7124 cms
arc of 90 degrees =4.74124 cms

Assuming that the angle at A is the right angle, Pythagoras' theorem says that the length of the hypotenuse (the side opposite the right angle) is the square root of the sum of the squares of the other two sides. In your case, AB and AC are 'the other two sides' and BC is the hypotenuse, so:

/ 2 2 /
length BC = V 10 + 20 = V 100 + 400


= V 500 = 22.36 cm

(To find the angle at C, you need trigonometry and is arc-tan(10/20)

and the angle at B is arc-tan(20/10) - 26.5 deg and 63.5 deg)

Diameter
US and Canadian penny, 19.05 mm
English penny, 20.30 mm

Circumference
US and Canadian penny, 59.85 mm
English penny, 63.77 mm

About 146 and a half degrees.

If this is homework, be sure to show your work.

Solve 50/360=15/c for c. The solution is c=360*15/50=100 cm

You can not do it unless you know the measure of the central angle sustending (supporting) the arc. If the angle is known, you use the proportionality relation that follows:
If angle is in degrees
(length of arc) / circumference=(measure of central angle sustending arc)/360.
Here the circumference is 2*PI*radius.

If angle is in radians , the relation is somewhat simpler,
arc length= (radius length)* (angle measure in radians)
It is clear that in the last relation, the unit for the arc length is the same as the unit for the radius.

If the distance of a person from a tower is 100 m and the angle subtended by the top of the tower with the ground is 30o, what is the height of the tower in meters? Solution:

• AB = distance of the man from the tower = 100 m
  
  
• BC = height of the tower = h (to be calculated)
  
  
• The trigonometric function that uses AB and BC is tan A , where A = 30o.

So tan 30o = BC / AB = h / 100 Therefore height of the tower h = 100 tan 30o = (100) 1/√3 = 57.74 m.

If an arc is 4╥, it is 12.56.
You can use 12.56 as a starting point and figure out what circumference that is 40° of.

Circumference = 2 • π • radius = π • diameter

Reverse this and you will have your answer.

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