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
zhuklara [117]
3 years ago
9

Please show the working and answer. you can take a picture for the working.

Mathematics
1 answer:
baherus [9]3 years ago
8 0

Answer:

(a) The area of the triangle is approximately 39.0223 cm²

(b) ∠SQR is approximately 55.582°

Step-by-step explanation:

(a) By sin rule, we have;

SQ/(sin(∠SPQ)) = PQ/(sin(∠PSQ)), which gives;

5.4/(sin(52°)) = 6.8/(sin(∠PSQ))

∴ (sin(∠PSQ)) = (6.8/5.4) × (sin(52°)) ≈ 0.9923

∠PSQ = sin⁻¹(0.9923) ≈ 82.88976°

Similarly, we have;

5.4/(sin(52°)) = SP/(sin(180 - 52 - 82.88976))

Where, 180 - 52 - 82.88976 = ∠PQS = 45.11024

SP = 5.4/(sin(52°))×(sin(180 - 52 - 82.88976)) ≈ 4.8549

Given that RS : SP = 2 : 1, we have;

RS = 2 × SP = 2 × 4.8549 ≈ 9.7098

We have by cosine rule, \overline {RQ}² =  \overline {SQ}² +  \overline {SR}² - 2 × \overline {SQ} × \overline {SR} × cos(∠QSR)

∠QSR and ∠PSQ are supplementary angles, therefore;

∠QSR = 180° - ∠PSQ = 180° - 82.88976° = 97.11024°

∠QSR = 97.11024°

Therefore;

\overline {RQ}² =  5.4² +  9.7098² - 2 ×  5.4×9.7098× cos(97.11024)

\overline {RQ}² ≈ 136.42

\overline {RQ} = √(136.42) ≈ 11.6799

The area of the triangle = 1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

By substituting the values, we have;

1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

1/2 × 6.8 × (4.8549 + 9.7098) × sin(52°) ≈ 39.0223 cm²

The area of the triangle ≈ 39.0223 cm²

(b) By sin rule, we have;

\overline {RS}/(sin(∠SQR)) = \overline {RQ}/(sin(∠QSR))

By substituting, we have;

9.7098/(sin(∠SQR)) = 11.6799/(sin(97.11024))

sin(∠SQR) = 9.7098/(11.6799/(sin(97.11024))) ≈ 0.82493

∠SQR = sin⁻¹(0.82493) ≈ 55.582°.

You might be interested in
A loan of $900 will be repaid in 36 installment of $30.22 each .what is the finance charge for the loan
Marat540 [252]

i hope this is what you are looking for but 36 times 30.22 equals 1087.92 subtract from 900 which is $187.92

<h2>$187.92 for finance charge for loan</h2>
8 0
3 years ago
Help please will mark brainliest!!!
solniwko [45]

Answer:

945

Step-by-step explanation:

8 0
3 years ago
Pattern A follows the rule "add 3" and Pattern B follows the rule "add 4." Pattern A 1 4 7 10 13 Pattern B 5 9 13 17 21 Which or
IceJOKER [234]

Answer:

(1,5) (7,13) (10,17) (7,13)

Step-by-step explanation:

1 4  7  10  13

5 9 13 17 21

6 0
2 years ago
Hellpppppppo asappppppppppopp plzzzzz
astra-53 [7]

Answer:

Step-by-step explanation:

radius = d/2=22/2=11

area=pi*r*r=22/7*11*11

=380.28

6 0
3 years ago
Read 2 more answers
How to solve 2x-8y=16
Darina [25.2K]
The answer of your question is x - 4 y=8
3 0
3 years ago
Other questions:
  • 20 POINTS! WILL GIVE BRAINLIEST!
    8·1 answer
  • In the diagram GH bisects ∠FGI
    11·1 answer
  • The tail of the spider monkey is 64% of 55in.What is the length of its tail?
    8·1 answer
  • - 30 = 5 ( x + 11 ) x =
    13·1 answer
  • Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with
    11·2 answers
  • What is the domain of f(x) = -(x-6)^2-30
    6·1 answer
  • Factor the trinomial x^2+10x+16
    11·2 answers
  • 24.5 x 24.5 x 3.14
    14·1 answer
  • Question 2 of 10
    9·1 answer
  • Find The slope of the line that passes through the point (2,4) ,(3,8)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!