Time and Tide wait for none

Geometry Level 1

You are solving problems at Brilliant.org. When you look at the clock,the time is 11 11 hours and 30 30 minutes. What is the angle \text{angle} between those hours and minutes point?

18 0 ∘ 180^\circ 15 0 ∘ 150^\circ 9 0 ∘ 90^\circ 16 5 ∘ 165^\circ

Nazmus Sakib by Nazmus sakib , 24, Bangladesh

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1 solution

The hour hand moves 0. 5 ∘ 0.5^\circ per minute and the minute hand moves 6 ∘ 6^\circ per minute.

At 11 : 30 11:30 , the hour hand had moved [ 11 ( 60 ) + 30 ] ( 0.5 ) = 34 5 ∘ [11(60)+30](0.5)=345^\circ

and the minute hand had moved ( 30 ) ( 6 ) = 18 0 ∘ (30)(6)=180^\circ .

The angle (smaller angle) between them is 345 − 180 = 345-180= 16 5 ∘ \color{#D61F06}\boxed{165^\circ} .

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