3: 40 formed an obtuse angle because 3:30 is a right angled triangle i.e 90⁰ but 3:45 is a straight line which is 180⁰. But 3:40 is less than 180⁰ but greater than 90⁰ which is an obtuse angle.
At 4:30, the minute hand is at 6, or 30°×6=180° from 12. At the same time (4:30), the hour hand is at 30°×4+30×30÷60 =120°+15° =135° from 12
So, the two hands of the clock (minute and hour hands) make an angle of 180°-135° =45° Which is an acute angle (an angle that is greater than 0°, but less than 90°). (FB: Nnenna Nnanna)
3: 40 formed an obtuse angle because 3:30 is a right angled triangle i.e 90⁰ but 3:45 is a straight line which is 180⁰. But 3:40 is less than 180⁰ but greater than 90⁰ which is an obtuse angle.
ReplyDeleteAt 3.40, the angle between the hour hand and the minute hand forms an angle of 130⁰.
ReplyDeleteHere’s how:
Total angle - 360⁰
1 hour - 60 minutes
Angle per minute - 360/60 = 6⁰
Now, the minutes hand is at 40 minutes, we multiply it by the degree per minute i.e 40×6 = 240⁰
Since the clock has 12 hours, we need to find the angle per hour too i.e 360/12 = 30⁰
From 12 to 3 is 3 hours, so:
3 hours × 30⁰ = 90⁰
The hour hand is actually between 3 and 4, and since we are looking at 3.40, we know that the hour hand is about 2/3 of an hour.
So, 90 + 2/3 × 30 = 110⁰
Therefore, the angle at 3.40 = |110| - |240| = |-130|
Which is the same as 130⁰
Phew! You gerrit? If you don't gerrit, go and solve your own. 😁😁😁
(FB: Nsikak Jack)
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ReplyDeleteEach division of the clock (i.e. between 1 and 2, 2 and 3, and so on) has an angle of = 360/12 = 30 degrees
ReplyDeleteIn one minutes the minute hand has travelled through an angle of 360/60 = 6 degrees
In one minute the hour hand travels through an angle of 30/60 = 0.5 degrees
At 3:40 the hour hand is between 3 and 4, exactly at 3 * 30 + 40 * 0.5 = 90 + 20 = 110 degrees from 12 o’ clock position
At 3:40 the minute hand is at 40 * 6 = 240 degrees from 12 o’clock position
Therefore at 3:40 the angle between hour and minute hands = 240 - 110 = 130 degrees.
At 4:30, the minute hand is at 6, or 30°×6=180° from 12.
ReplyDeleteAt the same time (4:30), the hour hand is at 30°×4+30×30÷60
=120°+15°
=135° from 12
So, the two hands of the clock (minute and hour hands) make an angle of
180°-135°
=45°
Which is an acute angle (an angle that is greater than 0°, but less than 90°).
(FB: Nnenna Nnanna)