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
Dahasolnce [82]
3 years ago
7

Find the obtuse angle between the following pair of straight lines.

Mathematics
1 answer:
ioda3 years ago
6 0

Given:

y=-2

y=\sqrt{3}x-1

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

y=mx+b     ...(i)

where, m is slope and b is y-intercept.

The given equations are

y=0x-2

y=\sqrt{3}x-1

On comparing these equations with (i), we get

m_1=0

m_2=\sqrt{3}

Angle between two lines whose slopes are m_1\text{ and }m_2 is

\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|

Putting m_1=0 and m_2=\sqrt{3}, we get

\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|

\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|

\tan \theta=\pm \sqrt{3}

Now,

\tan \theta= \sqrt{3} and \tan \theta=-\sqrt{3}

\tan \theta= \tan 60^\circ and \tan \theta=\tan (180^\circ-60^\circ)

\theta= 60^\circ and \theta=120^\circ

120>90, so it is an obtuse angle and 60, so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

You might be interested in
Find the slope of the line passing through the points<br> (-6,-5) and (4,4)
marshall27 [118]

Answer:

\frac{9}{10}

Step-by-step explanation:

The slope formula is  m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Here, x_{1} is -6, x_{2} is 4, y_{1} is -5, and y_{2} is 4.

m=\frac{4+5}{4+6}

m=\frac{9}{10}

So, the slope of the line passing through the points (-6,-5) and (4,4) is \frac{9}{10}.

3 0
3 years ago
Plz help!! Will give 30 points!!
Inessa [10]

Answer:

B) 12

Step-by-step explanation:

C is the circumference, d is the diameter, and r is the radius.  They are related by the following equations:

d = 2r

C = πd = 2πr

If d = 6.0, then r = 3.0.

If C / C' = 0.25, then:

(2πr) / (2πr') = 0.25

r / r' = 0.25

3 / r' = 0.25

r' = 12

8 0
3 years ago
Read 2 more answers
(01.05 LC)
Brums [2.3K]
I think it is c. Hope this helps!
5 0
3 years ago
-4(9 + 6) = plz help me
Arlecino [84]

Greetings, the answer is 11.

5 0
3 years ago
Read 2 more answers
If 4.5 pounds of cherries cost $10, what is the unit price per pound
djverab [1.8K]
Simply divide $10 by 4.5 to get the answer $2.22 per pound (actually the 2's keep repeating.  
I guess the store might charge $2.23 since some will round any overage to the next penny.
3 0
3 years ago
Other questions:
  • Triangle DEF is similar to triangle ABC, and the length of EF is 5cm. What are the lengths of sides DE is 6cm and DF is 8cm cent
    10·1 answer
  • What is the measure of angle DEF to the nearest degree?
    6·1 answer
  • Solve 4^5x = 16^2x-1
    15·2 answers
  • Harper wrote the expression 15-6+7 to represent "15 minus the sum of 6 and 7". Evaluate 15 - 6 + 7 and then exposing why Harper'
    5·1 answer
  • a hotel survey shows that nearly 30% of the guest staying at the hotel were there for personal reasons. the remainder of the gue
    10·2 answers
  • Rewrite in factored form. g(x)=2x^2+10x+12
    14·2 answers
  • Need help with this question asap please please
    11·1 answer
  • A temperature of F degrees Fahrenheit is the same as 5/9
    10·2 answers
  • Please Help, I don't understand how I get one of the answers below
    10·1 answer
  • Factor 169-4d^2 and identify the perfect square
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!