Question

the angle between hour hand and minute hand in clock at quarter past eleven in degree is​

Answer 1

Step-by-step explanation:

The angle between the hours hand and minutes hand in such a situation will be 90°.

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Answer 2

The angle between hour hand and minute hand at 11:15 is 112.5°.

Step-by-step explanation:

Given:

• A clock shown quarter past eleven.

To find:

• Find the angle between hour hand and minute hand.

Solution:

Step 1:

Write the time.

Quarter past means quarter of hour is passed.

An hour have 60 minutes,

Quarter of an hour $\frac{60}{4} = 15$

Thus,

Quarter past eleven means 11:15

Step 2:

Find the angle of hour hand.

For every hour, hour hand moves 30°,

$\because \: \frac{360}{12} = 30$

For every minute hour hand moves 0.5°

$\because \frac{360}{12 \times 60} = 0.5$

Hour hand moves =$11 \times 30 + 15 \times 0.5$

or

$= 330 + 7.5$

or

$= {337.5}^{ \circ}$

Whenever the calculated angle is more then 180°, we must subtract from 360°.

Thus,

Angle moved by hour hand $= {360}^{ \circ} - {337.5}^{ \circ}$

or

Angle moved by hour hand is $\bf {22.5}^{ \circ}$

Step 3:

Find angle moved by minute hand.

Minute hand moves 6° for every minute passed.

Thus,

For 15 minutes it rotates $= 15 \times 6$

or

$= {90}^{ \circ}$

Minute hour rotates 90°.

Step 4:

Calculate angle between hour hand and minute hand.

Add both the angles.

The angle between hour hand and minute hand at 11:15 is ${22.5}^{ \circ} + {90}^{ \circ}$

or

$= {112.5}^{ \circ}$

Thus,

The angle between hour hand and minute hand at 11:15 is 112.5°.

Learn more:

(i) The angle between hour hand and minute hand at 2:30 is ……….

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