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
alexgriva [62]
3 years ago
14

Given: △ABC, m∠A=60°

Mathematics
1 answer:
Anon25 [30]3 years ago
8 0

Answer:

Perimeter = 32.3

Area = 95.24

Step-by-step explanation:

Given:

△ABC, m∠A=60°

m∠C=45°, AB = 9

To find:

Perimeter of △ABC

Area of △ABC

Solution:

Using angle sum property in a triangle:

m∠A + m∠B + m∠C = 180°

m∠B = 180° - 45° - 60° = 75°

As per Sine Rule:

\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}}  = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08

\Rightarrow \dfrac{AC}{0.96}  = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22

Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = <em>32.3</em>

<em></em>

Area of a triangle is given as:

\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)

\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}

You might be interested in
Prime factorization of 43
Volgvan

Answer:

Step-by-step explanation:

Prime factorization: 43 is prime. The exponent of prime number 43 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 43 has exactly 2 factors.

8 0
3 years ago
Would appreciate someone’s help :)
Marrrta [24]

Count the squares

Side 1:5

Side 2:7

Side 3: 5

Side 4: 7

4 0
3 years ago
Solve for y 3x-4y=10
Georgia [21]
3x-4y=10

or,4y=3x-10
or,y=(3x-10)/4

so,y=3/4 x-5/2
5 0
3 years ago
Read 2 more answers
I really need help. I've been stuck on this question for almost an hour.
S_A_V [24]
Ma=Mc is the correct answer
8 0
3 years ago
Which rationale best describes why the functions are inverses? The functions intersect each other The functions have the same ge
Oksana_A [137]

Answer: It was the third answer. C.

7 0
3 years ago
Read 2 more answers
Other questions:
  • How to solve -x^2-2x=5
    15·2 answers
  • Help me I need help!!!!!!!!!
    5·1 answer
  • A number that is begins divided
    5·1 answer
  • #41.
    5·1 answer
  • Which inequality statement describes the two numbers on a number line?
    9·2 answers
  • One landscaper works 1.5 times as fast as another landscaper. Find their individual times if it takes 9 hours working together t
    13·1 answer
  • Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds
    10·2 answers
  • **URGENT**
    7·1 answer
  • 20 Points for 4 questions. BRAINLIEST also
    11·1 answer
  • John needs to hire a painter. Painter A is offering his services for an initial fee of $150 in addition to $12 per hour. Painter
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!