maths --plse help me..

posted by .

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 beta)/(tan beta - tan alpha)

  • maths --plse help me.. -

    make a sketch, label the height as h
    distance from last position to the tower as x

    tan (alpha) = h/(x+a)
    h = (x+a)tan alpha

    in the same way
    h = xtan beta
    (x+a)tan alpha = xtan beta
    x tan alpha - xtan beta = - a tan alpha
    x(tan alpah - tan beta) = -a tan alpha
    x = -a tan alpha/(tan alpha - tan beta)
    x = a tan alpha /(tan beta - tan alpha)

    h = xtan beta
    = a tan alpha * tan beta/(tan beta - tan alpha)
    as requested

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 51°30'. …
  2. Trig

    The angle of elevation from a point on the ground to the top of a tower is 37deg5'. The angle of elevation from a point 120 feet farther back from the tower is 29deg5'. Find the height of the tower (to the nearest foot).
  3. 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?
  4. Math

    If an observer stands at a certain point in the same horizontal plane as the base of a radio tower. the angle of elevation of the top of the tower is 13deg 15'. If the observer moves 156.25 feet towards the tower, the angle of elevation …
  5. trigonometry

    Mickey determines that the angle of elevation from his position to the top of the tower is 52°. He measures the angle of elevation again from a point 47 meters farther from the tower and finds to be 31°. Both positions are due East …
  6. Trigonometry damon plz help

    If the angle of a h meters long tower is in a straight line between two observers A and B angle of elevation of the top of the tower from A and B are alpha and beta respectively and AB=D meters find h/d
  7. trigo

    to calculate the height of the tower david measured the angle of elevation of the top of the tower from point A to B 42degrees. He moved then 30meter closer to the tower and from the point B the angle of elevation to the top of the …
  8. Maths

    From a point on a ground the angle of elevation from a tower is observed to be 60 degree. From a point on 40meter vertically above the first point of observation the angle of elevation from a tower is 30degree. Find the height of the …
  9. math

    PQ is a tower standing vertically on the horizontal ground. from A, the angle of elevation of top P of the tower is 45°. On moving 50 m. up a slope of 15°, the angle of elevation of P is found to be 75° from B. The horizobtal through …
  10. math

    pq is a tower standing vertically on the horizontal ground. from a, the angle of elevation of top p of the tower is 45°. on moving 50 m. up a slope of 15°, the angle of elevation becomes 75° from b. find height of the tower

More Similar Questions