Find the time between 2 and 3 when angle is 50 between hour and minute hands

Summary

In this educational video, Anil Kumar introduces a strategy to solve problems involving the angle between clock hands. He presents a formula to calculate this angle and applies it to find the time between 2:00 and 3:00 PM where the angle is 50 degrees. The explanation covers two possible scenarios and uses the formula theta = |30H - 11/2M| to find two solutions: 2 hours and 20 minutes or approximately 2 hours and 1/9 of a minute. The video is designed to help viewers understand how to approach such problems and encourages them to engage with the content.

Takeaways

• 🕒 The video discusses a method to find the angle between clock hands at a specific time.
• 🔍 The specific question is to find the time between 2:00 and 3:00 PM where the angle is 50 degrees.
• 📐 Each hour on the clock represents an angle of 30 degrees, and each minute represents 6 degrees.
• 🤔 The presenter explains that there could be two solutions, one where the hour hand is ahead of the minute hand and another where it's behind.
• 📘 The formula to calculate the angle between the clock hands is given by theta = |30H - 11/2M|.
• 🕗 For the given problem, H (hours) is between 2 and 3, and the angle theta is 50 degrees.
• 🧮 The presenter solves for M (minutes) using the formula and finds two possible times.
• 🕒 The two solutions are approximately 2 hours and 20 minutes or 2 hours and 1/9 of a minute.
• 🔗 A link is provided for the derivation of the formula used to calculate the angle.
• 👋 The presenter encourages viewers to comment, share, like, and subscribe for more content.

Q & A

What is the main topic of Anil Kumar's video series?

The main topic of Anil Kumar's video series is strategies to solve questions, with a specific focus on finding the angle between clock hands.

What is the general formula provided to find the angle between clock hands?

The general formula provided is theta equals 230 times H minus 11/2 times M, where H is the hour and M is the minutes.

What is the specific question Anil Kumar is trying to solve in the script?

The specific question is to find the time between 2:00 and 3:00 p.m. where the angle between the hour and minute hand is 50 degrees.

How does Anil Kumar explain the angles on a clock?

Anil Kumar explains that each position on the clock represents an angle of 30 degrees, starting from the 12 o'clock position.

What does Anil Kumar mean when he says there could be two solutions to the problem?

Anil Kumar means that there could be two times within the hour where the angle between the clock hands is 50 degrees, one where the minute hand is ahead of the hour hand and another where it is behind.

What is the significance of the number 30 degrees in the context of the clock?

The number 30 degrees signifies the angle between each hour mark on the clock face.

How does Anil Kumar use the formula to find the minutes (M) when the angle (theta) is 50 degrees?

Anil Kumar uses the formula by substituting theta with 50 degrees and H with 2 hours, then solving for M in two scenarios: when the minute hand is ahead and when it is behind the hour hand.

What are the two possible times that Anil Kumar finds where the angle between the clock hands is 50 degrees?

The two possible times are 2 hours and 20 minutes, and approximately 2 hours and 1/9 minutes.

What does Anil Kumar suggest at the end of the script for further understanding?

Anil Kumar suggests that viewers look at the derivation of the formula for a deeper understanding of how the formula is derived.

How does Anil Kumar encourage viewer interaction at the end of the script?

Anil Kumar encourages viewer interaction by inviting comments, asking viewers to share their views, and suggesting they like and subscribe to his videos.

Outlines

00:00

🕒 Understanding Clock Angles

Anil Kumar introduces a series on problem-solving strategies, focusing on a question about the angle between clock hands. He explains the general formula to find the angle between the hour and minute hands of a clock. The specific question is to find the time between 2:00 and 3:00 PM where the angle between the hands is 50 degrees. Anil uses a visual representation of a clock to clarify how each position on the clock represents 30 degrees, leading to a full circle of 360 degrees. He discusses the two possible scenarios where the minute hand could be either ahead or behind the hour hand to achieve the 50-degree angle. The formula provided is theta = |30H - 11/2M|, where H is the hour and M is the minute, to calculate the angle.

05:01

🔍 Solving for Time with Clock Angles

Anil Kumar continues the explanation by applying the formula to find the specific times between 2:00 and 3:00 PM where the angle is 50 degrees. He sets up two equations based on the formula, one where the minute hand is ahead and another where it is behind the hour hand. Solving these equations gives two possible times: 2 hours and 20 minutes or approximately 2 hours and 1/9 minutes (just shy of 2 minutes). Anil emphasizes that there are two solutions because the minute hand's position relative to the hour hand can vary. He concludes by offering a link for the derivation of the formula and encourages viewers to comment, share, and subscribe for more content.

Keywords

💡Angle

In the context of the video, 'angle' refers to the spatial relationship between the clock's hour and minute hands, measured in degrees. The video aims to find times when this angle is exactly 50 degrees. The angle is a fundamental concept in geometry and trigonometry, and in this video, it's used to solve a real-world problem related to timekeeping.

💡Clock hands

The 'clock hands' are the hour and minute indicators on a traditional analog clock. The video discusses the positions of these hands relative to each other to determine the angle between them. This is crucial for solving the problem of finding the time when the angle is 50 degrees.

💡Formula

A 'formula' in the video refers to the mathematical expression used to calculate the angle between the clock hands. The formula given is theta = |30(H - 11/2M)|, where H is the hour and M is the minute. This formula is key to solving the problem as it provides a methodical approach to finding the desired time.

💡Degrees

In the video, 'degrees' is a unit of measurement for angles. The goal is to find the time when the angle between the clock hands is 50 degrees. Degrees are a standard unit in angular measurements and are integral to the mathematical calculations in the video.

💡Hour hand

The 'hour hand' is one of the two primary hands on a clock, used to indicate the hour. In the video, the position of the hour hand is critical in determining the angle with the minute hand. The video explores scenarios where the hour hand is between 2 and 3 o'clock.

💡Minute hand

The 'minute hand' is the other primary hand on a clock, used to indicate the minutes. The video discusses how the minute hand's position relative to the hour hand affects the angle between them, which is essential for finding the correct time.

💡Time

In the video, 'time' refers to the specific hours and minutes on a clock face. The main objective is to find the times between 2:00 and 3:00 PM when the angle between the clock hands is 50 degrees. Time is the central theme around which the video's problem-solving revolves.

💡Position

The 'position' of the clock hands is discussed in relation to the numbers on the clock face. Understanding the positions helps in visualizing and calculating the angle between the hands. The video uses positions to describe where the hands might be for the angle to be 50 degrees.

💡Solve

To 'solve' in the video means to find the solution to the problem of determining the time when the angle between the clock hands is 50 degrees. The process involves using the formula and understanding the positions of the clock hands.

💡Derivation

The 'derivation' mentioned in the video refers to the process of obtaining the formula used to calculate the angle between the clock hands. The video promises to provide a link for the derivation, which would explain how the formula was developed.

💡Context

The 'context' in the video is the situation of finding a specific time on a clock where a certain angle exists between the hands. The context is crucial for understanding how the formula is applied to a real-world scenario involving timekeeping.

Highlights

Introduction to solving the angle between clock hands.

Question posed: Find the time between 2:00 and 3:00 p.m. where the angle between hour and minute hands is 50 degrees.

Explanation of the clock face and angles between the numbers.

Each hour on the clock represents a 30-degree angle.

Understanding the position of the hour and minute hands between 2 and 3 o'clock.

Two possible scenarios where the angle could be 50 degrees.

The minute hand could be either ahead or behind the hour hand.

The formula to calculate the angle between the clock hands: theta = 230 * (H - (11/2) * M).

The angle is always positive, so the formula takes the absolute value.

Substituting the known values (H = 2, theta = 50 degrees) into the formula.

Two equations are derived from the formula to find the minutes (M).

Solving for the minutes gives two possible solutions.

The two solutions are 2 hours and 20 minutes or 2 hours and 1/9 of 11 minutes.

The importance of considering both the minute hand being ahead or behind the hour hand.

The final answer is presented: two hours and either 20 minutes or approximately 2 minutes and 1/9 of 11 minutes.

A link will be provided for the derivation of the formula used.

Encouragement for viewers to comment, share views, like, and subscribe.

Transcripts

I'm Anil Kumar welcome to my series on

strategies to solve questions here's a

very interesting question based on angle

between clock hands I'll provide you

with a general formula to find the angle

between clock hands and then solve this

particular question the question here is

find the time between 2:00 and 3:00 p.m.

where the angle between hour and minute

hand is 50 degrees

so let's first try to understand the

situation let's say we have a clock here

and we want the time between 2:00 to

3:00 p.m. when the angle between the two

hands is 50 degrees so let's say this is

1 for us this is 2 that is 3 4 5 6 7 8 9

10 11 and 112 so one position could be

so as well as the angles are concerned

let's be very clear about and they say

if this is zero then the the angle from

here to the center we can say this each

is actually 30 degrees right so each is

30 degrees so 30 is 60 90 120 150 180

and so on right so that is how the

angles are so within every hour there is

30 minutes now we are saying find the

time between 2 to 3 hours that means we

want a situation where the hour hand is

somewhere between these two and the

minute hand is 50 degrees away to say

that our hand let's say is let's say

here for example right let's say our

hand is here in that case minutes and is

50 away so 50 away means two are 60

right so somewhere some

like this do you understand so we

exactly don't know where but somewhere

like this correct right so we need to

find this position we don't know what

this question is but that angle should

be fifty degrees that's what we need

agree

well one more situation could be that

this arm is on the other side right so

that is to say we could also have this

somewhere here right and somewhere there

some some position between two two three

and we could also have an angle of 50

degrees between the two so when we say

that the angle is 50 degrees we are

actually looking for two solutions so in

one case the our hand is beyond

diminished and the other case which sand

is beyond the our hand you get an idea

correct now we also know from the speed

of our and the minutes hand that the

angle can be given by the formula theta

equals 230 times H minus 11 by 2 times 3

minutes and this angle is always

positive so we take a positive value

that is the absolute value of this right

so in our case we for sure know that H

is 2 hours between two so we will start

somewhere

more than 2 right but less than 3 so H s

2 we also know that theta is 50 degrees

using this formula we can write down 50

equals to absolute value 30 times 2

minus 11 over 2 minutes and then we can

find the minutes absolute value

basically means that we could solve for

two equations

all this inside all this inside could be

either positive 50 or negative 50 but

absolute value will be positive you get

the idea right so so we could write this

as 30 times 2 is 60 minus 1/2 of 2 M

equals 2 positive 50 or this could also

be 60 minus 11 by 2 M equals 2 minus 50

clear because absolute value of minus 50

is also 50 you get the idea right less

so so taking this to the right side we

get 60 minus 50 equals to 11 by 2 m and

that is 10 and then we'll multiply by 2

over 11 to get the value of M correct so

that is 20 by 11 which is 1 and 11 when

you take away you get 9 over 11 minutes

okay on this side we have 60 plus 15

equals to 11 over 2 M or we could say

110 times 2 over 11 equals to M and that

gives you M equals 2 this goes 10 times

M equals to 20 right so we have two

solutions here one of the time could be

to 20 right the other will be to 1/9 by

11 minutes right so slightly very close

to two minutes right so basically I

should write two hours and so many

minutes right so many minutes two hours

extra two hours and so many minutes is

that clear so it is two hours and 20

minutes in this case correct so that is

how you could actually solve this

question so that that should be I think

clear and straightforward now to look

into this I'll provide you with a link

- for the derivation of this formula how

do we get this formula as the angle

theta being equal to 30 times hours - 11

by 2 times minutes perfect but I hope

that helps you to understand that the

idea here is to find two different

solutions right

since the minutes arm could be before

hours or after hours of and then solve

it hope it makes sense feel free to

write your comment share your views and

if you like and subscribe to my videos

at P great thanks for watching and all

the best