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Naya [18.7K]
3 years ago
14

Please tell me the correct answer and I will mark you brainliest

Mathematics
1 answer:
RoseWind [281]3 years ago
8 0
All of the answers you put are correct. good job!
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Given: △ABC, m∠A=60°
Anon25 [30]

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}

8 0
3 years ago
Blaize is filling a 20,000-gallon swimming pool. If 7040 gallons have already been filled, and the water is entering the pool at
Svetlanka [38]
We can start with subtracting 7040 from 20,000, getting us 12960 gallons remaining, If 720 gallons per hour are coming, we can make the equation 12960 = 720h, with h as hours. Next, we can divide both sides by 720, getting us 18. It will take 18 hours to fill the pool.
3 0
3 years ago
A sphere with a radius of 5 cm fits inside a box. Every face of the box is tangent to the sphere. What is the ratio of the volum
BARSIC [14]
Volume of box with side length of 5 = 5^3 = 125

Volume of sphere = (4/3)*pi*5^3 = (4/3)pi * 125

Ratio = 125/(4pi/3)*125  = 1/(4pi/3) = 3/(4pi)

Answer: B
8 0
3 years ago
Read 2 more answers
24r3-64r2-21r+56 answer
antiseptic1488 [7]
The answer is: (3r-8)(8r^{2}-7)
5 0
3 years ago
Find the area of the figure.<br> PLS I NEED HELP FAST I BEG YOU!
Nina [5.8K]
585 is correct!

LxWxH is for area

Mark with crown!
6 0
3 years ago
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