Post a New Question

Trigonometry

posted by .

frrom outlook tower 80ft. high, a man observes from a position 6.5ft. below the top of the tower that the angle of elevstion of the top of certain tree is 12deg40mins and the angle of depression of its base is 72deg20mins. If the base of the tower and the base of the tree are at the same level, what is the height of the tree?

  • Trigonometry -

    The line of sight of the 72 deg angle
    is represented by the hyp. of a rt triangle. The ht. of the observer above
    the bottom of tree represents the ver.
    side of the triangle.The hor. side is
    the dist. from the tree to the bottom
    of tower.The line of sight of the 12
    deg. angle is the hyp of a 2nd rt.
    triangle. Its' hor. side is = to hor.
    side of 1st triangle.

    Tan(72,20min) = 73.5 / X,
    X = 73.5 / Tan(72,20min) = 23.41 Ft.
    = hor. dist. from tree to tower.

    Tan(12,40min) = Y / 23.41 ,
    Y = 23.41 * Tan(12,40min) = 5.26 Ft
    = ver. side of 2nd triangle.
    h = 73.5 - 5.26 = 68.2 Ft. = ht.
    of tree.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math!

    From the top of a 40m fire tower, a fire ranger observes smoke in tower locations. One has a an angle of depression of 10o, and the other has an angle of depression of 7o. Calculate the distance between the smoke sightings when they …
  2. trigonometry

    From lookout tower 80ft. high, a man observes from a position 6.5 ft. below the top of the tower that the angle of elevation of the top of the certain tree is 12deg40mins and the angle of depression of its base is 70deg20mins. If the …
  3. trig

    Two office towers are 43m apart. From the top of the shorter tower, the angle of elevation to the top of the taller tower is 26o while the angle of depression to the base is 51o. Determine the height of each tower and round your answers …
  4. math

    From a lookout tower 80 ft. high, a man observes from a position 6.5 ft. below the top of the tower that the angle of elevation of the top of a certain tree is 12 degrees 40 minutes and the angle of depression of its base is 72 degrees …
  5. 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?
  6. math

    two office towers are 31 m apart. From the top of the shorter tower, the angle of elevation to the top of the tall tower is 25 degrees . The angle of depression to the base of the taller tower is 31 degrees. Calculate the height of …
  7. math trigonometry

    two office towers are 31 m apart. From the top of the shorter tower, the angle of elevation to the top of the tall tower is 25 degrees . The angle of depression to the base of the taller tower is 31 degrees. Calculate the height of …
  8. Math

    from a lockout tower 25 meters high, a man observes from a position 1.70 meters below the top of the tower that the angle of elevation of the top of a nearby building is 12 degrees 40 minutes and the angle of depression of its base …
  9. Trig

    Bob the ranger is atop a fire tower that i son the side of a mountain.The fire tower is 10 meters high and the angle of depression from the top of the tower to the base of the mountain is 48 degrees. The tower creates a 115 degree …
  10. Trigonometry

    At a point on the ground 125 ft from the base of a tower, the angle of elevation to the top of the tower has a degree measure of 38 degrees. How high is the tower

More Similar Questions

Post a New Question