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
emmainna [20.7K]
3 years ago
15

Line segment AB has a length of 15 and angle a=35degrees . A segment with a length of 12 will form the third side of the triangl

e. What are the possible measures of the angle opposite side AB? Please explain the process.
Mathematics
1 answer:
PtichkaEL [24]3 years ago
7 0

Answer:

C = 45.8 or C = 117.69

Step-by-step explanation:

Remark

Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.

Given

AB = 15

<A = 35

point C opposite line AB such that CB = 12 These givens give a unique answer.

Solution

Sin(35) / 12 = Sin(C) / 15                     Multiply both sides by 15

15*Sin(35) / 12 = Sin(C)                       Find 15/12

1.25*sin(35) = Sin(C)                           Write Sin(35)

1.25*0.5736 = Sin(C)                          Multiply the left

0.71697 = Sin(C)                                 Take the inverse Sin

C = 45.805 degrees                          This is the angle opposite AB

Angle B = 180 - 35 - 45.805 = 99.2

Ambiguous Case                    

If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.

I will set up the Sin law for you, and let you solve it

Sin(B) / 12 = Sin(35)/15

When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees

C = 180 - 35 - 27.31 = 117.69

So that's two values that C could have. I think that's all given these conditions.

Two Cases or None

<A = 35 degrees

AC = 15

CB = 12

This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.

You might be interested in
Factoring 2m^2 + 10m+25
oksian1 [2.3K]
Oh...........sorry?
///
5 0
3 years ago
You withdraw $29.79 from your bank account. Now your balance is −$20.51. Write and solve an equation to fi nd the amount of mone
Lunna [17]
You had $9.28 prior to making the withdrawal

-$20.51 = x - $29.79
x = $9.28
4 0
3 years ago
Read 2 more answers
I'm not sure can someone help me !!!
xz_007 [3.2K]
Turn it into transcript, It's upside down and I can't see it properly.
7 0
3 years ago
One of the psychologist's findings is that 18 months after the workshop, a sample of 49 job seekers who received training on set
IceJOKER [234]

Answer:

The psychologist finds that the estimated Cohen's d is 0.583.

Step-by-step explanation:

The Cohen's d is used to calculate the effect size, appied when a null hypothesis is rejected.

It can be calculated for this case of population mean as:

d=\dfrac{M-\mu}{\sigma}=\dfrac{6.5-5.8}{1.2}=\dfrac{0.7}{1.2}=0.583

The psychologist finds that the estimated Cohen's d is 0.583.

8 0
3 years ago
Write each quadratic expression in standard form. Draw a diagram if needed.<br> (x+4)(x-1)
12345 [234]

Answer:

The standard form of the quadratic equation is x² + 3·x - 4 = 0

Step-by-step explanation:

The standard form of a quadratic equation is a·x² + b·x + c = 0

Given that the expression of the quadratic equation is (x + 4)·(x - 1) = y, we can write the given expression in standard form by expanding, and equating the result to zero as follows;

(x + 4)·(x - 1) = x² - x + 4·x - 4 = x² + 3·x - 4 = 0

The standard form of the quadratic equation is x² + 3·x - 4 = 0

The graph of the equation created with MS Excel is attached

4 0
3 years ago
Other questions:
  • Which equation results from adding the equations in this system?
    12·2 answers
  • 4/7 times a number minus 8.5 is no more than 11.5
    11·2 answers
  • How many times can 15 go into 19
    11·2 answers
  • How do I solve 27×36
    5·2 answers
  • Plzzzz help me but dont ansewer if you dont know it. 100 points
    7·2 answers
  • What is the area of the rectangular prism
    6·1 answer
  • A body builder consumed 4,400 calories yesterday. Today, he consumed 3,600 calories. What is the percent decrease in number of c
    15·1 answer
  • How do I solve the length of AC?​
    5·1 answer
  • WILL RECIEVE BRANILIEST IF ANSWERED CORRECT
    13·1 answer
  • PLEASE HELP !!!!! 2 - 19 = 2?<br> BTW BTS OUTSOLD AND PAVED THE WAY !!!!!!!!!!
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!