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The face of a clock is inclined at 30 degrees to the vertical. If the hour hand is in horizontal position at 3 o'clock, find the inclination of the hour hand to the horizontal at
a) 1 o'clock
b) 10 o'clock
c) the times between 4 o'clock and 5 o'clock when the two hands are at right angles
a) The clock is a circle, so the sum of the angles is 360 degrees.
The clock is divided equally in 12 equal angles. Then, the angle between each two o'clock is 360/12 = 30 degrees.
a) Now, the inclination between the 1 o'clock and 3 o'clock is 2*30 degrees = 60 degrees.
b) The inclination between 10 o'clock and 3 o'clock is 5*30 = 150 degrees.
c) Between the clock 4 and 5 , the angle is 15 degree from each (4 and 5 o'clock, then the angle from (3 o'clock) is 30 + 15 = 45 degrees.