I'm so confused with this, please help me! TRIGONOMETRY

Question

1-2. Roxy and Heaven are standing at the seashore 10 miles apart. The coastline is a straight line between them. Both can see tuhe same ship in the water. The angle between the coastline and the line between the ship and Roxy is 35 degrees. The angle between the coastline and the line between the ship and Heaven is 45 degrees.

1. How far is the ship from Roxy?
A. 6.18 miles B. 7.18 miles C. 8.18 miles D. 9.18 miles

2. How far is the ship from Heaven?
A. 5.82 miles b. 6.82 miles C. 7.82 miles D. 8.82 miles


3. Three boats are at the sea: C1, C2, and C3. The crew of b1 can see both b2 and b3. The angle between the line of sight to b2 and the line of sight to b3 is 45 degrees. If the distance between b1 and b2 is 2 miles and the distance between C1 and b3 is 4 miles, what is the distance between C2 and C3?
A. 2.80 miles B. 2.95 miles C. 3.80 miles D. 3.95 miles

4-5. Rox, Rix, Rax are comparing in their tents. If the distance between Rox and Rix is 153 feet, the distance between Rox and Rax is 201 feet, and the distance between Rix and Rax is 175 feet.

5. What is the angle of Rox with respect to Rix and Rax?
A. 54.35 degrees B. 55.35 degrees C. 56.35 degrees D. 37.degrees

6.What is the angle of Rax with respect to Rox and Rix?
A. 46.40 degrees B. 47.40 degrees C. 48.40 degrees D. 49.40 degrees

Answer 1

question 1:

the distance from ship is Roxy x

 

accroding sine theorem

 

10 / sin100 = x / sin45

            

              x = 7.18 miles

 

the answer we choose B

 

question 2:

 

the distance from ship to Heaven is y,

 

according to sine theorem

 

y/ sin35 = 10 / sin100

 

        y = 5.82 miles

 

the answer we choose A

 

 

question 4  and 5, you can solve it by yourself according to the cosin theorem

 

a²=b²+c²-2bc*cosA
b²=c²+a²-2ac*cosB
c²=a²+b²-2ab*cosC

Answer 2

1)  Draw the triangle formed by the ship, Roxy, and Heaven; be 

     sure to label the two known angles: 35° and 45°

     and the distance between Roxy and Heaven: 10 miles

 

    The angle made by the line from ship to Roxy and the line 

    made by ship to Heaven is  100°

 

    Let D be the the distance from the ship to Roxy;  using the 

    Law of Sines:

 

                              sin 45°/ D = sin 100°/ 10

 

                                      cross multiply

 

                          10( sin 45° ) = D (sin 100° )

 

      [ 10( sin 45°)] / sin 100°  = D

 

                                       7.18 = D

 

Answer is B = 7.18 miles

 

I am sure that the other problems are going to use either the

Law of Sines or the Law of Cosines to get the answers.   If you

need further help, let me know.   I will answer your questions!