Finding Angle A in a Circular Arc: A Physics Trigonometry Problem

[Arkronus]

Hello, I am currently in beginning physics and we are learning a lot about Trig onometry. A homework problem is really bugging me. Here's what it says:

Find the angle A, given the altitude and arc length of the figure shown:
(the picture is in the attachment and also some work i have done.)

 

[Arkronus]

testing if i can put the image on this post.
http://img222.imageshack.us/img222/6819/physicszw2.gif

 

[andrevdh]

I can also solve it only numerically for the ratio

$$\frac{\sin(A)}{A}=0.719$$

which gives A as 0.8658 radians

 

[J77]

When you say you "believe the hypotenuse is the radius"... it doesn't look it in your sketch.

 

[HallsofIvy]

Basically, then, you have a circular arc, of length 4.17 cm. Dropping a perpendicular gives a length of 3 cm. Yes, the hypotenuse of the right triangle is a radius of the circle. sin A= 3/R and, as long as A is measured in radians, RA= 4.17. Since R= 4.17/A, putting that into the first equation you have sin A= 3A/4.17 just as you say. There is no "algebraic" way of solving such an equation. A numerical solution is the best you can do.