Expert: Steve Holleran - 2/25/2007

Question
---PROBLEM---
Suppose that a disc was thrown from point C and lands at point D. Instruments for measuring angles are located at points A and B. Point A is located 300 ft. west of point B and point C is located 100 ft. due north of point A. If a = 37 DEGREES and b = 62 DEGREES, find the distance that the disc was thrown.
Diagram -----> http://img03.picoodle.com/img/img03/7/2/24/f_diagramm_5052648.png

---NOTES---
I used the Law of Sines to find the distance from point B to D = 182.79 so roughly about 182.8ft[?]  

I then used the Law of Sines again to find the diagonal from point A to D = 268.18 so about 268.2ft[?]

And now, I'm a bit confused on how to find the distance from C to D? I am currently learning the Law of Sines and Law of Cosines so I think my teacher would prefer me to use these in part of the method. But in the Law of Sines, I would need at least 2 sides and 1 corresponding angle or 2 angles and 1 corresponding side..which I don't have? And I don't think the Law of Cosines can be applied here..or can it? Thanks!

Answer
Hello Kay,

You're doing great! and you're right on the money for finding CD.  The Law of Cosines DOES apply here, because you know AC=100, AD=268.2, and the included angle at A (angle CAD) is 53 degrees.

So, using the law of cosines, you get that CD = 222.82

It was a great help that you included the diagram!  I hope this helps you out.

Steve Holleran