A geometrical question please?

Question

I have a 90 degree arc that has a radius of 867 millimeters.

What is the linear distance of the arc?

Please show your work so I can pick up on the formula that I should have learned when not paying attention in Geometry class

"When am I ever going to need to know this stuff?" Famous last words.

Answer 1

The way I'm reading your problem is that the 90 degree arc is a segment of a circle. The circumference (arc length) of a circle is given by 2pi*r.

Since there are 360 degrees in a circle and the arc is 90 degrees, the arc length is actually 1/4 the circumference of the circle with an 867 mm diameter.

So S = 2pi*r/4 = 867pi/4 ~ 1361.88 mm

If you just want the distance of a line segment joining both ends of the arc then what you are looking for is the side of a triangle. As the arc is 90 degrees then a line from each endpoint is 867 mm to the center of the implied circle will meet and form a right angle. The line joining the end points is the hypotenuse of the triangle with the end points and center of the circle. Using the pythagorean theorem a²+b²=c² you have 2a²=c² since both lines are the same and with a=867mm c~1226.12.

Answer 2

If you're talking about the linear distance of the arc, you could just use the Pythagoreans theorem (a^2 + b^2 = c^2) with 867 mm for both side lengths. Your unknown would be the linear distance.

If you're talking about the arc length, use the formula a= r * (angle), where r is the radius and the angle is in radians.

Answer 3

sbjnyc's answer was absolutely correct, except for the answer. 2*(867)*pi / 4 = 1361.88

Answer 4

(2 x pi x r) / 4 =867mm
r = 551.72mm