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A tower 125 feet high stands on the side of a hill. At a point 240 feet from the foot of the tower measured straight down the hill, the tower subtends an angle of 25 degrees. What angle does the side of the hill make with the horizontal?

  • math -

    Draw a diagram.
    T = top of tower
    B = base of tower
    D = point 240' downhill
    draw a right triangle with hypotenuse TD. Let E be the right angle.

    From the law of sines,

    125/sin 25° = 240/sin ∠T
    ∠T is angle DTB
    ∠T = 54°
    Now you have angle T, since
    ∠TDB + ∠BDE + ∠DTB = 90°
    25° + ∠BDE + 54° = 90°

    ∠BDE = 11° is the angle you want.

  • math -

    how top draw the figure??

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