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
Rozlyn invested $2000 in an account that pays 4.25% annual simple interest. She will not make any additional deposits or withdra
PilotLPTM [1.2K]

Answer:

$850

Step-by-step explanation:

Interest = Principal x Rate x Time

I = 2000(.0425)(10)

I = 850

3 0
3 years ago
2/10 + 7 = 10<br> two over 10 plus 7 equals 10<br> pls help me solve the enquality
koban [17]
If this is a true or false question, it’s false because 2/10 + 7 ≠ 10. the correct inequality would be 2/10 + 7 = 12.
4 0
3 years ago
Read 2 more answers
Janet and Jack are walking in a two-day event to raise money for charity. Janet asks a friend for a $7.50 donation, plus $0.10 f
il63 [147K]

Answer:

Step-by-step explanation:

A. 40

B. 28

C. 44

D. 25

3 0
3 years ago
in a small school, there are 60 boys and 80 girls. write down the ratio of the number of boys to the number of girls. give your
tester [92]
60:80
Simplest form = 3:4

3 0
3 years ago
What are the Zeros of the quadratic function below?*<br> 10 points
S_A_V [24]
It says it’s 5 points not 10 points!
3 0
3 years ago
Other questions:
  • 5+5(x+4)&lt;20 help me out thanks for the help
    14·1 answer
  • Consider a collection of n individuals. . Assume that each person’s birthday is equally likely to be any of the 365 days of the
    15·1 answer
  • The tailgate of the truck is 3 feet above the ground. The incline of a ramp used for loading the truck is 15° find the nearest t
    15·1 answer
  • Please help ⚠️⚠️⚠️⚠️⚠️
    6·1 answer
  • Question for Math.<br> What is 3x-1?
    7·2 answers
  • AR 2011
    14·1 answer
  • Robert can paint a certain wall in 4 minutes, while it takes Jack 12 minutes to paint the same wall. How long will it take Rober
    11·1 answer
  • 3.6.PS-11
    11·1 answer
  • Please help quickly! in a test!
    7·2 answers
  • Giving points and brainliest if you help me answer this question correctly!!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!