Calculating Stream Width from AB to Point C | Law of Sines Application

[FawkesCa]

for God's sake...I NEED HELP!

Homework Statement

AB is a line 652 feet long on one bank of a stream, and C is a point on the opposite bank. A = 53° 18', and B = 48° 36'. Find the width of the stream from C to AB.

Homework Equations

law of sines

The Attempt at a Solution

ive proven all variables are correct (A,B,C and a, b, c). i come up with a height of 400.74ft. the answer book says its 345.45ft.
ive done this 6 times and come up with the same answer. am i a retard or should i just not go to Clark University (its their website)

 

[Mentallic]

I'm also getting the same answer as you, if you let the two angles be $$\alpha$$,$$\beta$$ and the distance across the bank be d, then the width of the river is given by

$$w=\frac{d}{cot(\alpha)+cot(\beta)}$$

and plugging in your values gives approx 400ft.

 

[cepheid]

I get the same answer as the OP as well. But there is some ambiguity as to what the angles are. The "A = some angle" and "B = some angle" statements really don't make sense, since A and B are just corners of the triangle. I assumed that "A" actually meant angle CAB, and that "B" actually meant angle CBA.

 

[Rasalhague]

Likewise, 400.739 ft., by

$$w = \frac{d \; \sin(\beta) \; \sin(\alpha)}{\sin(180^{\circ}-\alpha-\beta)}$$

 

[Mentallic]

$$\sin(180^{\circ}-\alpha-\beta)=\sin(\alpha+\beta)$$

 

[Rasalhague]

Ooh, so it is. Goodbye pi! So long, minuses!

 

[Mentallic]

And with a little re-arrangement, bring on the cotangents that I used!

 

[FawkesCa]

thank you, thank you, THANK YOU! i guess clark university is not the best place to try and teach yourself trigonometry. all of you help me SOOOOOOO much.

 

[Mentallic]

i guess clark university is not the best place to try and teach yourself trigonometry.

Not necessarily. Pretty much every book is going to have a few typos in it, you just need to be prepared. If you are getting a different answer and are sure of yourself, then don't be so quick to disbelieve your own work. Leave it and ask your professor or here online.