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
oksian1 [2.3K]
2 years ago
15

Solve the Law of Cosine: c^2 = a^2+ b^2 - 2abcosC for cos C.

Mathematics
1 answer:
Andrew [12]2 years ago
6 0

Answer:

The Law of Cosine :  cos C = \frac{a^{2}+ b^{2}-c^{2}}{2ab}

Step-by-step explanation:

See the figure to understand the proof :

Let A Triangle ABC with sides a,b,c,

Draw a perpendicular on base AC of height H meet at point D

Divide base length b as AD = x -b   and    CD = x

By Pythagoras Theorem

In Triangle BDC             And     In Triangle BDA

a² = h² + x²     (  1  )                        c² = h² + (x-b)²

                                                      c² = h² + x² + b² - 2xb   ...(. 2)

From above eq 1 and 2

c² = (a² - x²) + x² + b² - 2xb

or, c² = a² + b² - 2xb                    .....(3)

Again in ΔBDC

cos C = \frac{BD}{BC}

Or, cos C = \frac{x}{a}

∴ x= a cos C

Now put ht value of x in eq 3

I.e, c² = a² + b² - 2ab cos C

Hence , cos C = \frac{a^{2}+ b^{2}-c^{2}}{2ab}      Proved   Answer

You might be interested in
Using the rules of exponents to evaluate or simplify. write without negative exponents. 1/4^-2​
jekas [21]
16 or 4^2

This is really saying is 1/(1/4^2)
3 0
3 years ago
a tree rhar is 8 feet tall is growing at a rate of 2 feet each year a tree is 13 feet tall is growing at a rate of 1 foot each y
Vlad [161]

Answer:

  5 years

Step-by-step explanation:

The shorter tree is 5 ft shorter, but is growing 1 ft/year faster. It will make up the difference of 5 ft in (5 ft)/(1 ft/year) = 5 years.

8 0
3 years ago
Someone pls help asap this is due tmrw !!<br><br> x - 3y = -12<br> 2x + 3y = 3
hram777 [196]

Answer:

Step-by-step explanation:

to solve this system of equations we will add them

x-3y=-12

2x+3y=3 now +3y-3y=0

3x=-12+3

3x=-9

x=-3

plug in the first equation

-3-3y=-12

-3y=-12+3

-3y=-9

y=3

4 0
2 years ago
Please help!!! <br> A(b) is a function.<br><br><br><br> A. True<br> B. False
vazorg [7]
Your answer is false If that Is for 2020
4 0
3 years ago
Read 2 more answers
Complete the inequality for this graph.<br> y ≤ [?]
Eduardwww [97]

y< 3

3 is the correct answer.

8 0
3 years ago
Read 2 more answers
Other questions:
  • After 3/4 of a minute a sloth has moved just 3/8 of a foot. What is the sloths speed in feet per minute?
    9·1 answer
  • Can someone please help me out I’m so lost !!!!!!!
    5·2 answers
  • Common ratio for 64,-16,4,-1
    13·1 answer
  • Hello everyone! Can you answer today's question​?
    12·2 answers
  • Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
    6·1 answer
  • Which principle must a government follow in order to be considered a<br> democracy?
    14·2 answers
  • She put out two more recovery tests smh
    8·1 answer
  • 2.
    8·2 answers
  • What is the area of a rectangle with a length of 9
    5·1 answer
  • What is an equation of the line that passes through the point (6, 6) and is parallel to
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!