# Math-Geometry

Find the angle that the hr hands and the mins hand made when it at 10:00:45.67

so it 10olock 00 min and 45.67 sec
and find the angles

Show works
it one of those clocks problem

-thanks

"Find the angle that the hr hands and the mins hand made when it at 10:00:45.67"

I think one of the first things to do would be to convert the 45.67 to 45 2/3 seconds.
Now lets note that 1min=1/60 of the clockface = (1/60)*360deg=6deg Let's try to make a ballpark estimate too. When it's 10:00 the hands are two hours or 1/6 of the clock face apart, so the angle is 1/6 * 360deg or 60deg. If the minute hand were on the one minute and the hour hand didn't move, then the hands would be exactly 66deg apart. Thus the angle A that we want is 60deg < A < 66deg.
Now how much does the minute hand move in that time? That is, what angle does it make with the 12 during that time?
Well, (45 2/3)sec/60sec * 6deg =
(1) (137/3*60)*6deg=(137/30)deg (this is approx 4.5deg).
Now how much does the hour hand move during that time? We should observe that 1rev of hour hand = 12revs minute hand, thus the hour hand travels 1/12 the distance of the minute hand in the same time period. This means the angle the hour hand makes with the 12 in that time period is
(2) 60deg - (1/12)(137/30)deg = 60deg - 137/360 deg
If we add (1) and (2) we get
60deg - 137/360 deg + (137/30)deg =
60deg + (11*137)/360deg =
(3) 64 67/360 deg
This is very nearly 64.2 deg, but the fraction (3) above is exact.
Unfortunately I see that I haven't left anything for you to do, so try to work another problem from your text, or modify this one slightly to make sure you can do the steps for yourself.

wow nice thanks

You're welcome, but I see I didn't leave any steps for you to do. Try working through a similar problem if it were 10:01:45 or something similar say. Make sure you can work and understand the steps for yourself.

1. 👍 0
2. 👎 0
3. 👁 223

## Similar Questions

1. ### Math

School is 2 miles from home along a straight road. The table shows your distance from home as you walk home at a constant rate. Time(mins): 10-20-30 Distnce(mi)1.5-1-0.5 1)Is the relationship in the table proportional? 2)Find your

2. ### Physics

A student presses a book between his hands, as the drawing indicates. The forces that he exerts on the front and back covers of the book are perpendicular to the book and are horizontal. The book weighs 32 N. The coefficient of

3. ### Calculus 1

Related Rates: The minute hand on a watch is 9 mm long and the hour hand is 6 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)

4. ### Calculus

On a certain clock the minute hand is 4 inches long and the hour hand is 3 inches long. How fast is the distance between the tips of the hands changing at 4 pm?

1. ### math

A runner times herself to see how long it takes her to run different distances. The table shows the runner's times (in minutes) for running several distances (in miles). Miles: 1|2|3|4|6|8|10|12 Time: 7|16|30|35|57|75|106|132

2. ### Math - Trig

Hi I have a Trig question that i don't understand, can someone please explain how to solve for it using cosine law?? A Clock with a radius of 15 cm has an 11 cm minute hand and a 7 cm hour hand. How far apart, to the nearest

The minute hand on a watch is 7 mm long and the hour hand is 4 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)

4. ### Physics

Consider the 667 N weight held by two cables shown below. The left-hand cable had tension T2 and makes an angle of θ2 with the ceiling. The right-hand cable had tension 540 N and makes an angle of 55◦ with the ceiling. The

1. ### calculus

If the hands on a clocktower's clock are 2ft and 3ft long, how fast is the distance between the tips of the hands of the clock changing at 9:20? I know that the derivative of the minute hand is pi/30 rad/min and derivative of the

2. ### trigonometry - kindly help, needed badly

From a point on the bank of a stream,the angle of elevation of a tree top on the opposite bank is 38 degrees and 23 mins. And from a point 200.6 ft. straight back from the bank, the angle of elevation of the tree top is 20 degrees

3. ### physics

The hour hand and the minute hand for the famous Parliament clock tower Big Ben in London are 2.7m and 4.5m long and have masses of 60kg and 100kg, respectively. Calculate the total torque due to weight of these hands about axis

4. ### trigonometry

from a second-storey window directly across the street. the angle of elevation of the top of an office building is 67 degre 30 mins. and the angle of depression of the base 18 degre 20 mins. if the building are 38 meter apart. wat