trigonometry(height and distance)

The shadow of a tower when the angle of elevation of the sun is 45 degree is found to be 5m longer when it is 60 degree. Find the height of the tower.

  1. 👍 0
  2. 👎 0
  3. 👁 251
  1. How about starting with a diagram.
    Label the tower as PQ, with Q on the ground.
    Label the point with angle 45° as A, and the point with the 60° angle as B.
    You now have two right-angled triangles, PAQ and PBQ

    let BQ be x
    then tan60 = PQ/x ---> PQ = xtan60 = √3 x
    and tan 45 = PQ/(x+5) ---> PQ = (x+5)tan45 = (x+5)(1)

    so √3 x =x+5
    √3 x - x = 5
    x(√3 - 1) = 5
    x = 5/(√3-1)
    then PQ = √3(5/(√3-1)) = appr 11.83 m

    or

    look at triangle PAB, angle PBA = 120° making angle APB = 15°
    by the sine law:
    PB/sin45 = 5/sin15
    PB = 5sin45/sin15

    in triangle PBQ,
    sin60 = PQ/PB
    PQ = PBsin60 = (5sin45/sin15)(√3/2) = appr 11.83

    In my experience, most students find the second method easier to follow

    1. 👍 0
    2. 👎 0
  2. Ans is correct can you show me fig.

    1. 👍 0
    2. 👎 0
  3. We can't put diagrams on here, I think you should be able to follow my directions. I described the diagram.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    two points A and B 80 ft. apart lie on the same side of a tower and in a horizontal line through its foot. if the angle of elevation of the top of the tower at A is 21 degree and B is 46 degree, find the height of the tower.

  2. Math

    The angle of elevation of the top of house from the bottom of a tower 160m high is 26 degree.From the top of the tower the angle of elevation is 24 degree.What is the height of the house if the tower and the house are 50m apart?

  3. maths

    The angle of elevation of the top of a tower from a point is 42m alwayfrom its base on level ground is 36 degree. Find the hight of the tower

  4. math

    the angle of elevation of the sun is 27 degree.a man is 180cm tall.how long is his shadow?give your answer to the nearest 10cm.

  1. math

    A flagpole at right angle to the horizontal is located on a slope that makes an angle of 12∘ with the horizontal. The pole's shadow is 16 meters long and points directly down the slope. The angle of elevation from the tip of the

  2. 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

  3. trig

    a tower that is a 200 meters is leaning to one side. from a certain point on that side, the angle of elevation to the top of the tower is 70 degree. From a point 55 meters closer to the tower, the angle of elevation is 85 degree.

  4. trigonometry

    the angle of elevation of a tower at place A south of it is 30degrees and at B west of A and a distance of 50 from it the angle of elevation is 18degrees, determined the height of the tower

  1. mathematics

    Cand D are two observation posts on the same horizontal ground at the foot A of a vertical tower AB.the tower is 18m due north of D and 24m east of C.the angle of elevation of B from D is 35¡ã.calculate to three s.f the height

  2. physics

    1) The angle of elevation to the bottom of a transmission tower on a hill from an observer standing 1.8 km away from the base of the hill is 5 degrees. The angle of elevation to the top of the tower from the tower is 6.8 degrees.

  3. math

    the shadow of an electric pole is 5m long when the angle of elevation of the sun is 60 degree .find the length of the shadow when the angle of elevation of the sun is 45 degree.

  4. MATH

    13. A tree casts a shadow of 17 ft. The angle of elevation from the tip of the shadow to the top of the tree is 68°. To the nearest foot, what is the height of the tree? 14. The angle of depression of a diver from the boat is

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