PRE-CALC HELP

1) Two boats leave the same port at the same time. One travels at a speed of 27 mi/h in the direction N 50° E and the other travels at a speed of 22 mi/h in a direction S 70° E (see the figure). How far apart are the two boats after one hour? (Round your answer to the nearest mile.)

2) A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 58°. A guy wire is to be attached to the top of the tower and to the ground, 150 m downhill from the base of the tower. The angle α in the figure is determined to be 7°. Find the length of cable required for the guy wire. (Round your answer to the nearest meter.)

Thank you!

  1. 👍
  2. 👎
  3. 👁
  1. #1
    convert to rectangular coordinates and subtract to get a distance of 24.9

    #2
    assuming the angle α is the angle between the ground and the cable, then using the law of sines, the distance d of the cable is

    d/sin148° = 150/sin35°

    1. 👍
    2. 👎
  2. 1. x^2 = 22^2+ 27^2 -2(22)(27)cos60

    x^2 =1213 -1188cos60

    x^2 =619
    x= 24.9 miles

    1. 👍
    2. 👎
  3. kuai's solution is better, because the assignment is evidently involving the law of sines/cosines.

    also, less work!

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    a boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 3:00 pm. at what time were the two boats closest together

  2. math

    A ship leaves port and travels 21km on a bearing of o32 degrees and then 45km on a bearing of 287 degrees. a. calculate its distance from the port. b. calculate the bearing of the port from the ship

  3. Maths

    Two boats A and B left a port C at the same time on different route .B travelled on a bearing of 150 degree and A travelled 8km and B had travelled 10km ,the distance between the Two boats was found to be 12km .calculate the

  4. Pre calculus

    A ship leaves port A and travels 60 miles due west to point C. It then adjusts its course 37 degrees northward. It travels 98 miles in that direction until it reaches port B. What angle with respect to due north could the ship

  1. math

    Two ships leave a port at 9 a.m. One travels at a bearing of N 53° W at 12 miles per hour, and the other travels at a bearing of S 67° W at 19 miles per hour. Approximate how far apart they are at noon that day. (Round your

  2. trig

    Help! Ships A and B leave port at the same time and sail on straight paths making an angle of 60 degrees with each other. HOw far apart are the ships at the end of 1 hour if the speed of ship A is 25 km/h and that of ship B is 15

  3. math

    Two boats leave a port at the sametime. The first travels at 15km/hr on a bearing of 135 degree. While the second travels at 2km/hr on a bearing of 63 degree . If after 2hours the second boat is directly North of the first boat,

  4. Maths

    A ship leaves a port and travels 21km on a bearing of 32 and then 45km on a bearing of 287 calculate its distance from the port and the bearing of the port from the ship

  1. Physics Grade 11

    Two people are fishing from small boats located 28 m apart.Waves pass through the water, and each person’s boat bobs up and down 15 times in 1.0 min. At a time when one boat is on a crest, the other one is in a trough, and there

  2. Mathematics

    Two boats A and B leave port P at the same time. Boat A sails 30km in the North east direction and boat B sails 20km on a bearing of 300 degrees. What is the distance between the two boats and what is the bearing of boat A from

  3. math

    A boat leaves a port at 10AM traveling at a speed of 30 mi/h in the direction N50°E. Another boat leaves the same port at the same time traveling at a speed of 26 mi/h in the direction S70°E. How long does it take for the boats

  4. Algebra

    two ships leave the same port at the same time. One travels north at 12 miles per hour. The other travel west at 5 miles per hour. After four hours, how far apart are the two ships?

You can view more similar questions or ask a new question.