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  • What time does the clock show when the hour hand is between 3 and 4 and the angle between the two hands of the clock is 50°?  

What time does the clock show when the hour hand is between 3 and 4 and the angle between the two hands of the clock is 50°?

 

Answers (1)

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We use the formula to find the angle between the hands of a clock:

Angle \(=|30 H-5.5 M|\)

\(H=3\) (between 3 and 4)

We are given: Angle \(=50^{\circ}\)

Now plug in the values:

|30 \times 3-5.5 M|=50 \Rightarrow|90-5.5 M|=50

Case 1:

90-5.5 M=50 \Rightarrow 5.5 M=40 \Rightarrow M=\frac{40}{5.5}=\frac{80}{11} \approx 7.27 \text { minutes } \Rightarrow \text { Time } \approx 3: 07: 16

Case 2:

90-5.5 M=-50 \Rightarrow 5.5 M=140 \Rightarrow M=\frac{140}{5.5}=\frac{280}{11} \approx 25.45 \text { minutes } \Rightarrow \text { Time } \approx 3: 25: 27

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Divya Sharma

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