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mel-nik [20]
1 year ago
7

Given triangle ABC, A=105°, a=10cm, b=7cm, find B,C and c.

Mathematics
1 answer:
Whitepunk [10]1 year ago
4 0

The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

<h3>What is law of cosine?</h3>

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

                                        C = 32.49°

We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

Learn more about law of cosines here:

brainly.com/question/17289163

#SPJ1

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Three consecutive integers add to 567. Find the integers. PLEASE HELP
Aleks04 [339]
Consecutive integers mean one after the other and their difference would one more or less.

Let the numbers be x, x +1, x +2.

Therefore x + (x+1) + (x +2) = 567
               3x + 3 = 567
               3x = 567 -3 = 564
               3x = 564  Divide by 3.
                 x  = 564/3
                 x  = 188
Therefore integers  x, x +1, x +2 = 188, 188+1, 188+2.
                                                =  188, 189, 190.
Cheers.
7 0
2 years ago
At breakfast, restaurant charges $2 for the first cup of orange juice and then $1 for each refill which graph represents this si
liq [111]

Answer:

line

Step-by-step explanation:

y= 2+(x-1)*1= x+1

y=x+1

linear function, the graph is going to be a line

6 0
3 years ago
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for the decimal 0.555 the value of the digit in the tens place is how many times as much as the value of the digit in the thousa
NNADVOKAT [17]
The value of the digit in the tens place is 100 times as much as the value of the digit in the thousands place.
7 0
3 years ago
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Find the values of x and y. Pls helpI’m helpless at math
Svetradugi [14.3K]

Answer:

  • x = 1
  • y=\frac{\sqrt{3}}{2}  

Step-by-step explanation:

From the given right-angle triangle

The angle = ∠60°

  • The adjacent to the angle ∠60° is 1/2.
  • The opposite to the angle ∠60° is y.

The hypotenuse = x

<u>Determining the value of x:</u>

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = 1/2 and hypotenuse = x

cos\:60^{\circ }=\:\:\frac{\frac{1}{2}}{x}

\cos \left(60^{\circ \:}\right)=\frac{1}{2x}

\frac{1}{2}=\frac{1}{2x}          ∵ cos (60°) = 1/2

2x=2

Dividing both sides by 2

\frac{2x}{2}=\frac{2}{2}

Simplify

x=1

Thus, the value of hypotenuse x is:

x = 1

<u>Determining the value of y:</u>

Using the trigonometric ratio

sin 60° = opposite / hypotenuse

As we have already determined the value of hypotenuse x = 1

substituting opposite = y and hypotenuse = 1

sin 60° = y/1

y = 1 × sin 60°

y=\frac{\sqrt{3}}{2}       ∵  \sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}

Therefore, the value of y is:

y=\frac{\sqrt{3}}{2}      

Summary:

  • x = 1
  • y=\frac{\sqrt{3}}{2}    
5 0
3 years ago
35 POINTS. I need help! Please!
topjm [15]
There is no solution  for the first one

if you eliminate y   you get 2 equations
-13x - 13z = -25
-13x - 13x = -15    

- there is no solution to theses

a23  means the element in the second  row and the 3rd column

so its -5 
7 0
3 years ago
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