Math

Two fire towers are 30 kilometers apart, tower A being due west of tower B. A fire is spotted from the towers, and the bearings from A and B are E 14 degrees N and W 34 degrees N, respectively. Find the distance d of the fire from the line segment AB.

  1. 👍 0
  2. 👎 0
  3. 👁 1,291
asked by Mike
  1. 1. Draw line segment AB.

    2. Draw the 14-degree angle from point
    A.

    3. Draw the 34-degree angle from point B. Label the intersection of these 2 lines point C. Now we have formed
    triangle ABC.

    4. Draw the altitude from point C perpendicular to AB and label it CD.

    The distance of the fire from AB is
    equal to the altitude(CD).

    A + B + C = 180 Deg.
    14 + 34 + C = 180,
    C = 132 Deg.


    a/sinA = c/sinC,
    a/sin14 = 30/sin132,
    Multiply both sides by sin14:
    a = 30sin14 / sin132 = 9.77km.

    CD = 9.77sin34 = 5.46km = dist. from
    fire to AB.

    1. 👍 0
    2. 👎 0
    posted by Henry
  2. 21.9

    1. 👍 0
    2. 👎 1
    posted by sam
  3. 1. Call the point where d intersects AB point C.
    2. Let CB equal x.
    3. cot(14)= (30-x)/d
    cot(34)= x/d
    4. cot(14)= (30/d)- (x/d)
    cot(14)= (30/d)- cot(34)
    cot(14)+ cot(34)= (30/d)
    d(cot14+ cot34)= 30
    d = 30/ (cot14+ cot34)
    d = 5.46 km

    1. 👍 0
    2. 👎 0
    posted by Arpita
  4. Sorry this one's easier to read.
    1..
    Call the point where d intersects AB point C.

    2..
    Let CB equal x.

    3..
    cot(14)= (30-x)/d
    cot(34)= x/d

    4..
    cot(14)= (30/d)- (x/d)
    cot(14)= (30/d)- cot(34)
    cot(14)+ cot(34)= (30/d)
    d(cot14+ cot34)= 30
    d = 30/ (cot14+ cot34)
    d = 5.46 km

    1. 👍 0
    2. 👎 0
    posted by Arpita

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trig application

    I worked this problem out but I do not fully understand what I am doing. Fire tower A is 30 kilometers due west of fire tower B.. A fire is spotted from the towers, and the bearings from A and B are N 76 degrees E and N 56 degrees

    asked by Hutch on February 21, 2015
  2. Math-SineLaw

    Fire lookout towers are used to locate fires so they can be put out as soon as possible. These towers often work in networks and if two towers can see a fire at the same time, they can determine the location of the fire vey

    asked by Sydney on June 5, 2016
  3. Trigonometry

    Two fire towers are 30 km apart, tower A being due west of tower B. A fire is spotted from the towers, and the bearings from A and B are E 14° N and W 34° N, respectively. Find the distance d of the fire from the line segment

    asked by AwesomeGuy on February 4, 2013
  4. math

    Two fire towers, A and B, are 20.3 km apart. From tower A, the compass heading for tower B is S80E. The ranger in each tower sees the same forest fire. The heading of the fire from tower A is N50E. The heading of the fire from

    asked by math123 on March 4, 2016
  5. Functions

    Two forest fire towers, A and B, are 20.3 km apart. From tower A, the bearing of tower B is 70 degrees. The ranger in each tower observes a fire and radios the bearing of the fire form the tower. The bearing from tower A is 25

    asked by Chuck on March 23, 2015
  6. Math

    Two fire towers, A and B, are 20.3 km apart. From tower A, the bearing of tower B is 70̊. The ranger in each tower observes a fire and radios the bearing of the fire from the tower. The bearing from tower A is 25̊ and from tower

    asked by Pam on December 19, 2008
  7. Trigonometry (Law of Sine)

    Fire towers A and B are located 10 miles apart. They use the direction of the other tower as 0°. Rangers at fire tower A spots a fire at 42°, and rangers at fire tower B spot the same fire at 64°. How far from tower A is the

    asked by Alianne on February 25, 2012
  8. Trigonometry (Law of Sine)

    Fire towers A and B are located 10 miles apart. They use the direction of the other tower as 0°. Rangers at fire tower A spots a fire at 42°, and rangers at fire tower B spot the same fire at 64°. How far from tower A is the

    asked by Alianne on February 25, 2012
  9. math

    From a fire tower, A, a fire is spotted on a bearing of N42°E. From a second tower, B, the fire is on a bearing of N12°W. The two fire towers are 23 km apart, and A is N63°W of B. How far is the fire from each tower? Just need

    asked by Anonymous on August 3, 2018
  10. Pre-Calculus

    I need help with this problem: The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65 degrees E, and the two towers are 30 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80

    asked by Sharon on April 2, 2008

More Similar Questions