Homework Help: geometry

Posted by Samuel on Thursday, May 3, 2012 at 5:01pm.

A park maintenance person stands 16 m from a circular monument. Assume that her lines of sight form tangents to the monument and make an angle of 47°. What is the measure of the arc of the monument that her lines of sight intersect? Please don't just answer it tel me how to do it. Thanks :)

geometry - Henry, Friday, May 4, 2012 at 7:59pm
P = 47 Deg.
Arc AB is the Arc Intercepted by P.
Arc ACB is The remainder of the circle.

AB = 360 - ACB.
(ACB-AB)/2 = P
Substitute 360-ACB for AB
(ACB-(360-ACB))/2 = 47
Multiply both sides by 2:
(ACB-(360-ACB)) = 94
ACB-360+ACB = 94
2ACB-360 = 94
2ACB = 94+360 = 454
ACB = 454/2 = 227 Deg.

AB = 360-ACB = 360-227 = 133 Deg.

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