trigonometry

a surveyor finds that from Point A on the ground the angle of elevation to the top of a mountin is 23 degrees. when he is at point B that is 1/4 closer to the base of the mountain the angle of elevation is 43 degrees. how high is the moutnain? One mile =5280 feet. (Assume that thr base of the mountain and the two observation points are on the same line.)Give answer to the nearest foot.

  1. 👍
  2. 👎
  3. 👁
  1. tan23 = Y/X,
    Y = Xtan23,

    tan43 = Y/(X-.25).
    Y = (X-0.25)tan43.

    y = Xtan23 = (X-0.25)tan43,
    Xtan23 = (X-0.25)tan43,
    Xtan23 = Xtan43-0.25tan43,
    0.4245X = 0.9325X-0.2331,
    0.4245X-0.9325X = -0.2331,
    -0.508X = -0.2331,
    X = 0.4589 Miles.

    y = 0.4589tan23 = 0.1948 miles.

    Y = 0.1948mi * 5280ft/mi = 1029 Ft.
    = Height of mountain.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Precalculus

    To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 33 degrees. From a point that is 300 feet closer to the

  2. dynamic

    A projectile fired from the edge of a 150 m high cliff with an initial velocity of 180 m/s at an angle of elevation of 30 deg with the horizontal. i. The greatest elevation above the ground reached by the projectile. ii.

  3. Math

    A hot air balloon is observed from two points A and B on the ground A and B are 800 feet apart the balloon is east of both points the angle of elevation from A to the balloon is 37 degrees and the angle of elevation from B is 65

  4. trig

    A plane is flying at an elevation of 30000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 18. Find the distance between the plane and the airport. Find the distance

  1. Math

    1. A rangers tower is located 44m from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 28 degrees and the angle of depression to the base is 36 degrees. How tall is the tree? 2. An engineer

  2. Trig

    From a point P on level ground, the angle of elevation of the top of a tower is 27°10'. From a point 23.0 meters closer to the tower and on the same line with P and the base of the tower, the angle of elevation of the top is

  3. Mathematics

    The angle of elevation of the top of a flagpole from a point on the level ground is 30degrees. From another point on the ground 20m, nearer the pole the angle of elevation is 60degrees. Calculate the height of the pole?

  4. Pre-calculus

    A surveyor standing 62 meters from the base of a building measures the angle to the top of the building and finds it to be 38°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it

  1. trig

    a building 60 feet high. from a distance at point A on the ground, the angle of elevation to the top of the building is 40 degree. from a little nearer at point B, the angle of elevation to the top of the building is 70 degree.

  2. Trig

    From a point A on the ground, the angle of elevation to the top of a tall building is 24.1 degrees. From a point B, which is 600 ft closer to the building, the angle of elevation is measured to be 30.2 degrees. Find the height of

  3. Trigonometry

    The angle of elevation from a point on the ground to the top of a pyramid is 23^•(degree)40^’(minutes). The angle of elevation from a point 112 ft farther back to the top of the pyramid is 15^•30’. Find the height of the

  4. Spherical Trigonometry

    *Approximate the angle of elevation of the sun if a box 5 meters tall casts a shadow 4 meters long on level ground. *As a weather ballon rises vertically its angle of elevation from a point P on the level ground 110km.from the

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