Precal, please help asap!

The angles of elevation theta and alpha to an airplane from the airport control tower and from an observation post 2 miles away are being continuously monitored. If theta is 42 degrees when alpha is 81 degrees, how far is the plane from the observation post?

  1. 👍 0
  2. 👎 0
  3. 👁 238
asked by l
  1. You need to clarify the diagram. Label the airplane A, the tower T and the post P. The plane is at altitude h, with AP=t and AT=p. Point Q is directly below the plane. The distance PQ=q and thus TQ = 2-q.

    If the plane is between the tower and the post, then

    h/q = tanα
    h/(2-q) = tanθ

    Eliminate h and plug in the angles, and to get the desired distance t,

    q tan 81° = (2-q)tan42°
    6.31q = 0.90(2-q)
    q = 0.249
    so, h = 0.249*6.31 = 1.571

    t^2 = .249^2 + 1.571^2
    t = 1.59 miles

    If the plane is not between the two measurement locations, then you need to set up different triangles.

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    An airplane flies clockwise around an airport control tower at a speed of 190 m/s. If that control tower is 8 km from the airplane at all times, what is the plane’s angular velocity (magnitude and direction)?

    asked by M on October 6, 2014
  2. math

    From the top of the control tower 250 m tall, an airplane is sighted on the ground below. If the airplane is 170 m from the base of the tower, find the angle of depression of the airplane from the top of the control tower.

    asked by Daniela on February 20, 2017
  3. Math

    An airplane is flying 100 km north and 185 km west of an airport. It is flying at a height of 7 km A) what is the straight long distance to the airport? B) what is the angle of elevation of the airplane, from the point of view of

    asked by Sydney on June 15, 2016
  4. Math 11

    An airplane is flying 100 km north and 185 km west of an airport. it is flying at a height of 7 km. A) what is the straight-line distace to the airport? B) what is the angle of elevation of the airplane, from the point of view of

    asked by Priya on October 20, 2014
  5. geometry

    an airplane is flying 75km south and 35 km west of an airport. It is flying at a heigh of 6 km A)what is the straight-line distance to the airport? B)What is the angle of elevation of the airplane, from the point of of view of the

    asked by airplanes on March 2, 2012
  6. maths --plse help me..

    The angle of elevation of the top of a tower as observed from a point on the ground is alpha and on moving a meters towards the tower, the angle of elevation is beta .prove that the height of the tower is a (tan alpha*tan

    asked by Meenakshi on December 13, 2012
  7. Math

    At an airport, a flight controller is in a tower 45m above the ground. She observes an airplane flying at a constant altitude at an angle of elevation of 14 degrees from her line of sight. Seven seconds later, the airplane flies

    asked by BJ on May 31, 2012
  8. trig

    express 20sin theta + 4 cos theta as R sin(theta + alpha) R sin(theta + alpha) = R cos(alpha)sin(theta) + R sin(alpha)cos(theta) ----> Rcos(alpha) = 20 Rsin(alpha) = 4 The x-y coordinates of a point on a circle of radius R that

    asked by paul c on November 24, 2006
  9. trig

    please am stucked help me.in the diagram below.A,B and C are three points in the same horizontal plane and DC is a vertical tower.AC=AB=x and D^C=DB.the angle of elevation of D from C is alpha and DB^C=theta

    asked by utlwanang on May 26, 2013
  10. geometry

    from an airplane flying 7000 feet above the ground the angle of depression to the base of the control tower is 19 degrees. find the distance from a point on the ground directly beneath the airplane to the control tower.

    asked by Anonymous on June 3, 2010

More Similar Questions