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Mrac [35]
3 years ago
13

The hour hand on a clock is 4 cm long, and the minute hand is 10 cm long. What is the exact distance between the tips of the han

ds at 10 o'clock?
Mathematics
1 answer:
Allushta [10]3 years ago
4 0

Answer:

2 sqrt(19)

Step-by-step explanation:

We know that the angle between the two hands

360 /12 *2 = 60 degrees

We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12

This is a triangle where we know 2 sides and the angle between them.

We can use the law of cosines to determine the third side

c^2 = a^2 + b^2 -2abcosC

Where C is the angle between sides a and b

a =4 and b = 10  C = 60  and we are looking for side c

c^2 = 4^2 + 10^2 -2*4*10 cos60

c^2 =16+100 - 80cos 60

c^2 = 76

Take the square root of each side

sqrt(c^2) = sqrt(76)

c = sqrt(76)

c =sqrt(4) sqrt(19)

c =2 sqrt(19)


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Answer:

X=20.6666

Step-by-step explanation:

7 0
3 years ago
perimeter of parallelogram 140 cm if one side is longer than the other by 10cm, find the length of each of its parallel side
Verizon [17]

The length of each of its parallel side are 30 cm and 40 cm.

<u>Step-by-step explanation</u>:

  • Perimeter of parallelogram = 140 cm.
  • The one side of parallelogram = x cm.
  • The other side of parallelogram = x+10 cm.

Perimeter of a parallelogram = 2 (base+height)

⇒ 140 = 2(x+x+10)

⇒ 140 = 2(2x+10)

⇒ 140 = 4x+20

⇒ 4x = 120

⇒ x = 120/4

x = 30 cm

∴ The longer side = 30+10 = 40 cm

4 0
3 years ago
Evaluate 24nk if n= 6 and k = 8
saul85 [17]
<h2>1152</h2>

24nk

n=6

k=8

24 × (6) × (8)

24 × (48) = 1152

4 0
3 years ago
Read 2 more answers
You are considering 2 jobs. One job pays $350 per week plus 2% commission on all sales. The second job pays $1,200 per month and
jasenka [17]
If the year is 52 weeks long (the average amount of weeks in a year). 
$350.00*52= $18,200.00
$1200.00*12= $14,400.00 
2.5% of 1,000,000=25,000  
2% of 1,000,000=20,000  
$18,200.00+20,000= $38,200.00
$14,400.00+25,000= $39,400.00
The second (2nd) job pays better. 


3 0
3 years ago
Read 2 more answers
Question 27 <br> Find the length of the hypotenuse. Leave answer in simplest radical form.
skelet666 [1.2K]

Use SOHCAHTOA.  Since we are looking for the hypotenuse, you must use sine or cosine.  Since, we are given the adjacent side, use cosine.

cosx=a/h

cos45=8/h

√2/2=8/h

<em>*Cross multiply*</em>

h√2=16

<em>*Divide both sides by √2*</em>

h=16/√2

<em>*Multiply by √2/√2*</em>

h=(16√2)/2

<em>*Simplify the fraction*</em>

h=8√2

Hope this helps!!

6 0
3 years ago
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