1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
boyakko [2]
2 years ago
6

Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to

indicate exponents. For example, type a2 as a∧2. (Hint: Let s be a length of each side and x be the angle measure; then use these variables in the law of cosines. )
Mathematics
1 answer:
bekas [8.4K]2 years ago
3 0

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

<h3>Laws of cosines </h3>

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b^2 + c^2 - a^2)/2bc

cos B= (a^2 + c^2 - b^2)/2ac

cos C = (a^2 + b^2 - c^2)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s^2 + s^2 - s^2)/(2s×s)

cos A = (s^2 )/(2s^2)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s^2 + s^2 - s^2)/(2s×s)

cos B = (s^2 )/(2s^2)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s^2 + s^2 - s^2)/(2s×s)

cos C = (s^2 )/(2s^2)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

Learn more on The law of cosines here: brainly.com/question/2866347

#SPJ1

You might be interested in
A certain drug dosage calls for 17 mg per kg per day and is divided into two doses (1 every 12 hours). If a person weighs 255 po
vekshin1

Answer:

985.15mg

Step-by-step explanation:

Calculation for how many milligrams of the drug should he receive every 12 hours

First step is to calculate the weight in kg

255 lbs = 255/2.2 = 115.9 kg

Second step is multiply mg/kg in order to get total medicine per day

Dose per day=115.9kg × 17 mg

Dose per day= 1,970.3

Third step is to calculate how many milligrams of the drug should he receive by dividing the day dose by 2

Dose milligrams=1,970.3/2

Dose milligrams=985.15mg

Therefore how many milligrams of the drug should he receive every 12 hours will be 985.15mg

3 0
3 years ago
30 pts+
Veseljchak [2.6K]

Answer:

I dont know the answer I'm just scrolling down this app because I like going through my brothers phone exceptionally mommy and daddy wrestling

7 0
2 years ago
Need help don’t understand
adoni [48]

there is an equation for straight lines which goes

y-y,=m(x-x,)

where( x, , y, ) is any coordinate on the line and m is the gradient

so your answer is

y-7= -2(x-4)

does this make sense?

7 0
2 years ago
Read 2 more answers
6. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
kramer

Answer:

I think the answer is B. f(x) = -1/3x - 4

Step-by-step explanation:

Use the given functions to set up and simplify  

4−16.

XF(x)=X

Fx

1 − 7 = −6

2 − 10 = −8

3 − 13 = −10

4 − 16 = −12

8 0
3 years ago
PLZ I NEED HELP NOW!!!!!!!!!!!!!!!!!!!!
seropon [69]

Answer:

H, 20%

Step-by-step explanation:

960/4,800 = 20/100

8 0
3 years ago
Other questions:
  • I ate 7/8 of birthday cake.how much of cake has not been eaten?
    14·2 answers
  • What is the length of the hypotenuse of a right triangle if the legs are each 5 inches long?
    12·1 answer
  • Four ingredients costing $320 per kg $240 per kg $160 per kg and $85 kg are mixed so that air masses are in the ratio 4:1:3:2. c
    5·2 answers
  • Boris currently has a savings account. He saves $25 per month.
    8·1 answer
  • Find the percent of the quantity of 110% of 300​
    13·2 answers
  • I need help if anyone knows the answer please ASAP
    12·1 answer
  • 2x+1=(-3)<br>what is the value of x??????​
    5·1 answer
  • What rule must be applied when evaluating an expression in which the
    11·2 answers
  • helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
    7·1 answer
  • Solve the right triangle (all sides and angles) please help!!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!