On a horizontal ground, the base of a straight ladder is 6 m away from the base of a vertical pole. The ladder makes an angle of 45 degrees to the horizontal. If the ladder is resting at a point located at one-fifth of the height of the pole from the bottom, the height of the pole is ______ meters.
A. 15
B. 25
C. 30
D. 35
GATE 2019 · General Aptitude · Geometry · medium
Answer: Height of pole H = 30 m (Option C)
Find height the ladder reaches on the pole: tan(45 degrees) = height_reached / 6 => 1 = height_reached / 6 => height_reached = 6 m
Relate height reached to full pole height: 6 = H / 5 => H = 6 x 5 = 30 m