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
The number sentence 4×6=6×4 is what property
scZoUnD [109]
This will be commutative property. with the help of the equation a+b=b+a 
4 0
3 years ago
I need help with this
Debora [2.8K]
C because if you look at the intercept it’s a y and the y inception is equivalent to 4 so y=4x-14
5 0
3 years ago
PLEASE HELP I'LL MARK YOU BRAINLIEST IF YOU'RE CORRECT I don't understand this​
mario62 [17]
The y-intercept of the function is at y = -3 so the options that don’t include it are off the table. The only possible answer is option C. Option A doesn’t work because plugging in positive values would give negative numbers within the square root which isn’t defined in the real numbers.
8 0
2 years ago
Read 2 more answers
What is 9/80 in decimal?
Nookie1986 [14]
9/80 is equal to the decimal .1125
5 0
3 years ago
Read 2 more answers
A jar contains 900 beans. Of them, 700 are white beans and the rest are navy beans. What ratio of white beans to all the beans
Nikolay [14]

Answer:

700/900

Step-by-step explanation:

There are 900 beans in total.

There are 700 white beans

The ratio of white beans to all the beans is 700/900 or 700:900

5 0
3 years ago
Other questions:
  • PLEASE ANSWER I WILL GIVE YOU BRAINLIEST!
    14·2 answers
  • A certain 5-digit combination lock can be reset with a new combination. The lock uses numbers from 1 to 6. After a friend accide
    8·1 answer
  • If the original quantity is 8 and the new quantity is 6, what is the percent decrease?
    12·1 answer
  • Sarah has a solid wooden cube with a length of 4/5 centimeter. From each of its 8 corners, she cuts out a smaller cube with a le
    8·1 answer
  • Central school is hosting a "central has talent" show . They will award various prizes for the best 3 acts in the show . First p
    13·2 answers
  • What is the correct answer?
    11·1 answer
  • Evaluate 15/r -1 when r = 5
    15·2 answers
  • 14 POINTS!!!!!!<br> !!!!!!!!!!!!!!!!!!!!!!!!!!!!
    14·2 answers
  • CAN SOMEONE PLEASE HELP ME PLEASE
    7·1 answer
  • Consider the quadratic expression given below.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!