Law of Sines problems that involve a perpendicular

[KYPOWERLIFTER]

Could someone point me in the correct direction? I have no problem working out the angles and lines, but when one has to take into account the perpendicular, then I get confused. It is clear that the relationships are altered, but I am missing something? I have made worked further in the problem set but these two have me a bit mixed up. These are from a website, and as I have related I am trying to re-learn old math habits. Not a "homework" question, per se.

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.

In a triangle ABC, a = 700 feet, B = 73° 48', and C = 37° 21'. If M is the middle point of BC find the length of AM, and the angles BAM and MAC.

Homework Equations

SinA/a = SinB/b = SinC/c

The Attempt at a Solution

sin 53.3 (652)/sin 78.1 = a, the calculator claims 534.24'
then, cos 48.6 (534.24') = c, calculator reads 353.30' WRONG!

For the second one I worked to this point:

b = sin 73.8 (700')/sin 68.85 = 720.76', then sin 37.35 (720.76) = AM. . .I saw this wasn't correct. . .

 

[Mark44]

For the first problem, I agree that a = 534.24', but I disagree with your final value for the width of the stream. The relationship is sin(48.6 deg) = w/534.24, so w = 534.24 * sin(48.6 deg) = 400.74' (approx).

 

[Mark44]

For the second problem, after you have found b, you know MC and angle C, so you can use the law of cosines to find AM.

 

[KYPOWERLIFTER]

Eureka!

As for the second problem, I now get 490.75'. The answer given is 490.83'. I am thinking that is rounding difference. On the first problem, I have no idea why I used cos instead of sine. . . looking at too many problems, I suppose. However, the given answer is 345.43'. After I correct for my function error, I get the same figure that you do.

 

[Mark44]

I don't see how they get 345.43' for the first problem. I worked it again and got 400.74' again. It's possible that the book's answer is wrong. I don't automatically assume that when my answer is different from the book's answer, but answers in books are wrong from time to time.