At what time between 9 am and 10 am are the hands of a clock be in opposite direction
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Let me first share a formula with you,
θ=30H−112Mθ=30H−112M
This gives the angle between hour and minute hands of the clock at the given hour H and given minutes M.
Now, according to question, time has to be like 9:__9:__ and angle is 180∘180∘, since hands are in opposite direction. So, we need to calculate only minutes.
Using formula and data,
H=9,θ=180∘H=9,θ=180∘
180=30∗9−112∗M180=30∗9−112∗M
M = 16.36 min = 16 min 21.8 sec
θ=30H−112Mθ=30H−112M
This gives the angle between hour and minute hands of the clock at the given hour H and given minutes M.
Now, according to question, time has to be like 9:__9:__ and angle is 180∘180∘, since hands are in opposite direction. So, we need to calculate only minutes.
Using formula and data,
H=9,θ=180∘H=9,θ=180∘
180=30∗9−112∗M180=30∗9−112∗M
M = 16.36 min = 16 min 21.8 sec
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