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
sleet_krkn [62]
2 years ago
13

This is a geometry question, i need something quickly :)

Mathematics
1 answer:
Marysya12 [62]2 years ago
6 0

Answer:

hope it helps mark me brainlieast!

Step-by-step explanation:

<em>For triangle ABC with sides  a,b,c  labeled in the usual way, </em>

<em> </em>

<em>c2=a2+b2−2abcosC  </em>

<em> </em>

<em>We can easily solve for angle  C . </em>

<em> </em>

<em>2abcosC=a2+b2−c2  </em>

<em> </em>

<em>cosC=a2+b2−c22ab  </em>

<em> </em>

<em>C=arccosa2+b2−c22ab  </em>

<em> </em>

<em>That’s the formula for getting the angle of a triangle from its sides. </em>

<em> </em>

<em>The Law of Cosines has no exceptions and ambiguities, unlike many other trig formulas. Each possible value for a cosine maps uniquely to a triangle angle, and vice versa, a true bijection between cosines and triangle angles. Increasing cosines corresponds to smaller angles. </em>

<em> </em>

<em>−1≤cosC≤1  </em>

<em> </em>

<em>0∘≤C≤180∘  </em>

<em> </em>

<em>We needed to include the degenerate triangle angles,  0∘  and  180∘,  among the triangle angles to capture the full range of the cosine. Degenerate triangles aren’t triangles, but they do correspond to a valid configuration of three points, namely three collinear points. </em>

<em> </em>

<em>The Law of Cosines, together with  sin2θ+cos2θ=1 , is all we need to derive most of trigonometry.  C=90∘  gives the Pythagorean Theorem;  C=0  and  C=180∘  give the foundational but often unnamed Segment Addition Theorem, and the Law of Sines is in there as well, which I’ll leave for you to find, just a few steps from  cosC=  … above. (Hint: the Law of Cosines applies to all three angles in a triangle.) </em>

<em> </em>

<em>The Triangle Angle Sum Theorem,  A+B+C=180∘ , is a bit hard to tease out. Substituting the Law of Sines into the Law of Cosines we get the very cool </em>

<em> </em>

<em>2sinAsinBcosC=sin2A+sin2B−sin2C  </em>

<em> </em>

<em>Showing that’s the same as  A+B+C=180∘  is a challenge I’ll leave for you. </em>

<em> </em>

<em>In Rational Trigonometry instead of angle we use spreads, squared sines, and the squared form of the formula we just found is the Triple Spread Formula, </em>

<em> </em>

<em>4sin2Asin2B(1−sin2C)=(sin2A+sin2B−sin2C)2  </em>

<em> </em>

<em>true precisely when  ±A±B±C=180∘k , integer  k,  for some  k  and combination of signs. </em>

<em> </em>

<em>This is written in RT in an inverted notation, for triangle  abc  with vertices little  a,b,c  which we conflate with spreads  a,b,c,  </em>

<em> </em>

<em>(a+b−c)2=4ab(1−c)  </em>

<em> </em>

<em>Very tidy. It’s an often challenging third degree equation to find the spreads corresponding to angles that add to  180∘  or zero, but it’s a whole lot cleaner than the trip through the transcendental tunnel and back, which almost inevitably forces approximation.</em>

You might be interested in
Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
ryzh [129]

Answer:

x= 3 +\sqrt{23}, 3 -\sqrt{23}

Step-by-step explanation:

You use the quadratic formula to get x= \frac{18+6\sqrt{23} }{6} ,\frac{18-6\sqrt{23} }{6}

Then you simplify and get the answers x= 3 +\sqrt{23}, 3 -\sqrt{23}

​​  

​​  

6 0
3 years ago
Read 2 more answers
Help asap my last question GIVING BRAINLIST!!!!
Alex

Answer:

1) x < 0

2) x > 0

3) x < 10

4) x < -\frac{31}{55}

5) x \geq 0

6) x \geq -1

Step-by-step explanation:

1) -3 > 2x -3

2x- 3 < -3

2x - 3 + 3 < -3 +3

2x < 0

\frac{2x}{2} < \frac{0}{2}

x < 0

2) 5 > -x + 5

-x + 5 < 5

- x + 5 -5 < 5 - 5

-x < 0

\frac{-x}{-1} < \frac{0}{-1}

x > 0

3) \frac{x}{5} -2 < 0

5 \times (\frac{x}{5} - 2 ) \times 5 < 0

x - 10 < 0

x -10 + 10 < 0 +10

x < 10

4) -5x + 11 > 31

-5x \cdot 11 < 31

-55x < 31

\frac{-55x}{-55} > \frac{31}{-55}

x < -\frac{31}{55}

5) \frac{1}{2}x - 4 \geq -4

\frac{1}{2}x -4 +4 \geq -4 +4

\frac{1}{2}x \geq 0

\frac{\frac{1}{2}x }{\frac{1}{2} } \geq \frac{0}{\frac{1}{2} }

x \geq 0

6) -4x + 2 \leq 6

-4x +2 - 2 \leq 6 -2

-4x < 4

\frac{-4x}{-4} \leq  \frac{4}{-4}

x \geq -1

6 0
3 years ago
Hey can someone be nice enough to help me
BaLLatris [955]

Answer:true

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
A pedestrian walks 7.4 kilometers west
attashe74 [19]

Answer: 11.8 km

Step-by-step explanation:

The resulting figure is a right angled triangle shown below

$$Apply the Pythagorean theorem to find out the magnitude of the resultant vector $A B$ in the triangle $A B C$ as follows -$$\begin{aligned}&A B^{2}=B C^{2}+C A^{2} \text { (Hypotenuse }{ }^{2}=\text { Base }^{2}+\text { Adjacent }^{2} \text { ) } \\&=7.4^{2}+9.2^{2} \\&=139.4 \\&A B=11.806777 \\&\quad A B \approx 11.8 \mathrm{~km} \text { (Rounded off to the nearest tenth) }\end{aligned}$$

3 0
2 years ago
Round 1.530 to the nearest hundred​
Bumek [7]
1.53

Since it is 0 in the thousands place it, doesn’t change.
4 0
2 years ago
Other questions:
  • Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 ? 9x2 ? 108x + 2, [?3, 4]
    5·1 answer
  • On a coordinate plane, 2 trapezoids are shown. The first trapezoid has points A (negative 1, negative 2), B (1, negative 2), C (
    5·2 answers
  • The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.300.30​, and the sample statis
    8·1 answer
  • WILL MARK BRAINLIEST. NEED MATH HELP ASAP
    14·1 answer
  • Rita has 90 pages in her notebook. She uses 39 pages. How many pages are left in her notebook?
    8·2 answers
  • Nissa is going to plant 485 tree this year if nissa plants 5 orchards of trees how many trees will be in each orchard
    14·1 answer
  • The line y=-1/2x+3 is perpendicular to which line
    7·1 answer
  • Find the value of x.
    7·2 answers
  • 12 yards +14 feet by 2
    5·1 answer
  • Need help with this !!!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!