# Find the angle help

• Apr 21st 2008, 11:49 AM
viciouspoultry
Find the angle help
Ok I need help finding the angle and I attached a crude picture of the drawing. just to clarify the circles are tangent to one another and the ray that is created by the angle and the radii are perpendicular to the top of the ray. The radii are 2inches and 4 inches respectively.

The only thing I don't know is how to calculate the hypotenuse and/or the top ray to finish the problem.

• Apr 23rd 2008, 10:24 PM
earboth
Quote:

Originally Posted by viciouspoultry
Ok I need help finding the angle and I attached a crude picture of the drawing. just to clarify the circles are tangent to one another and the ray that is created by the angle and the radii are perpendicular to the top of the ray. The radii are 2inches and 4 inches respectively....

The two radii must be parallel because they are perpendicular to the same straight line. Therefore you can use proportions here:

$\frac x2 = \frac{x+6}4~\implies~ x = 6$

You are looking for the angle $2\alpha$ . Use the Sine function to calculate $\alpha$:

$\sin(\alpha) = \frac13~\implies~\alpha \approx 19.47...^\circ$

and therefore

$2\alpha \approx 38.94...^\circ$