# 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

We're asked
"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. 👍
2. 👎
3. 👁

## Similar Questions

1. ### 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

2. ### 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?

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. ### 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

1. ### Finite Math

A "hand" consists of a set of 5 cards selected from an ordinary deck of 52 cards: (1) How many different hands contain exactly 4 diamonds? = 27885 (2) How many different hands contain exactly 4 cards of the same suit (any of the

2. ### 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

3. ### 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

4. ### Algebra

How many hands of 5 cards can be made from a standard deck of cards such that each hand contains exactly 1 red card and 4 black cards?

1. ### 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

2. ### Cosine Law

The minute hand of a clock is 12 cm long, and the hour hand is 10cm long. Determine the distance between the tips of the hands at 9:30pm, to the nearest mm.

3. ### statistics

1. A professor measured the time (in seconds) required to catch a falling meter stick for 19 randomly selected studentsâ€™ dominant and non-dominant hand. The professor claims that the reaction time in an individualâ€™s dominant

4. ### math Please HElp

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.)