Question

Hi, I need help with these problems, I'm not sure where to start. The book's examples are different. Thanks in advance!!

1.) To find the distance AB across a river, a distance BC of 472m is laid off on one side of the river. It is found that B=108.1 degrees and C= 17.9 degrees. Find AB.

2.) Find the angle between the pair of vectors to the nearest tenth of a degree.
9i+2j, -3i+3j

3.) Vector v has the given magnitude an direction. Find the magnitude of the indicated component of v. Find the vertical component of v if:
theta=38.3 degrees. |v|= 281

Answer 1

1. angle A = 180-17.9-108.1 = 54°
now by the sine law:
AB/sin17.9 = 472/sin54
AB = 472sin17.9/sin 54
= ....

2. (9,2)dot((-3,3) = √85√18cosØ , where Ø is the angle between them
(-27 + 6)/(√85√18) = cosØ
I got Ø = 122.5°

sin 38.3 = y/281
y = ....

Answer 2

thank you