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
Rainbow [258]
3 years ago
5

Please help me with his math question ​

Mathematics
1 answer:
mr_godi [17]3 years ago
6 0

Answer:  ∠A = 55° (acute)

               ∠B = 105° (obtuse)

               ∠C = 86° (acute)

               ∠D = 114° (obtuse)

<u>Step-by-step explanation:</u>

Use Law of Cosines: a² = b² + c² - 2bc · cosA     for each of the angles.

Note that ∠B from each triangle will have to be added to solve for ∠B.

Similarly for ∠D.

For ΔDAB: a = 9.1, b = 7.3, d = 11

9.1² = 7.3² + 11² - 2(7.3)(11) · cosA

82.81 = 53.29 + 121 - 160.6 · cosA

-91.48 = -160.6 cosA

0.5696 = cos A

55° = A

b² = a² + c² - 2ac · cosB

7.3² = 9.1² + 11² - 2(9.1)(11) · cosB

53.29 = 82.81 + 121 - 200.2 · cosB

-150.52 = -200.2 cosB

0.7518 = cosB

41° = B

ΔDAB: ∠A + ∠B + ∠D = 180°

            55° + 41° + ∠D = 180°

                 96°    + ∠D = 180°

                              ∠D = 84°

*****************************************************

For ΔBCD: b = 8.2, c = 9.1, d = 4.6

b² = c² + d² - 2cd · cosB

8.2² = 9.1² + 4.6² - 2(9.1)(4.6) · cosB

67.24 = 82.81 + 21.16 - 83.72 · cosB

-36.73 = -83.72 cosB

0.4387 = cosB

64° = B                                        ∠B in ABCD = 41° + 64° = 105°

c² = b² + d² - 2bd · cosC

9.1² = 8.2² + 4.6² - 2(8.2)(4.6) · cosC

82.81 = 67.24 + 21.16 - 75.44 · cosC

-5.59 = -75.44 cosC

0.074 = cosC

86° = C      

d² = b² + c² - 2bc · cosD

4.6² = 8.2² + 9.1² - 2(8.2)(9.1) · cosD

21.16 = 67.24 + 82.81 - 149.24 · cosD

-128.89 = -149.24 cosD

0.8636 = cosD

30° = D                                        ∠D in ABCD = 84° + 30° = 114°

****************************************************************************

Acute angles are those that are less than 90°   --> ∠A & ∠C

Obtuse angles are those that are greater than 90°  --> ∠B & ∠D  

You might be interested in
Express the ratio below in its simplest<br> form 3:6:6
matrenka [14]

Answer:

1:2:2

Step-by-step explanation:

To simplify this ratio, you need to find a common factor to divide by. In this instance, that would be 3.

3 0
3 years ago
–41 – y = −17 linear equations by elimination ​
AfilCa [17]
I’m pretty sure y= 3
7 0
3 years ago
Read 2 more answers
Which of these sequences is a geometric sequence?
podryga [215]
3, 9, 27, 81, 343, 729, … is a geometric sequence because each term is obtained by multiplying 3 to the preceding term.
7 0
3 years ago
Read 2 more answers
Solve the equation 5m = -10
Alexxx [7]
Divide by 5 on both sides and the answer should be m= -5
8 0
3 years ago
Read 2 more answers
Jane earns a 5.5% commission on the selling price of each home she sells. She earned $9,020 in commission on the sale of a home.
ratelena [41]

Answer:

"$164000" is the appropriate answer.

Step-by-step explanation:

Let the selling price be "s".

As per the question,

If Jane take 5.5% of selling price i.e.,

= 0.055\times s

Given commission,

= $9,020

then,

The selling price will be:

⇒ 0.055\times s=9020

                s=\frac{9020}{0.055}

                   =164000 ($)    

6 0
2 years ago
Other questions:
  • A spinner used for a game is divided into 3 sections;yellow,brown and orange. Janie spins the spinner 18 times. The spinner land
    9·2 answers
  • Which of the following describes the decimal equivalent of 5/9? terminating decimal repeating decimal non-terminating, non-repea
    15·1 answer
  • Geometry help please i really appreciate it
    6·1 answer
  • A quality inspector must verify whether a machine that packages snack foods is working correctly. The inspector will randomly se
    13·1 answer
  • 3 more than 2 times a number
    5·1 answer
  • Round 325.6809 to the nearest hundredth. Enter your answer in the space<br> provided
    11·2 answers
  • 10. Does the mapping represent a function?
    14·1 answer
  • What is the Mean and the Median of this set of test scores?
    12·1 answer
  • PLEASE HELP ME
    5·1 answer
  • Complete the ratio table
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!