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3 years ago

I’ll mark you brainlist

Mathematics

2 answers:

Elan Coil [88]3 years ago

4 0

Y OVER X is the answer .

kherson [118]3 years ago

3 0

Answer:

Step-by-step explanation:

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Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o

Brrunno [24]

Answer:

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

$Sin\ C = \frac{h}{a}$

Make h the subject:

$h = aSin\ C$

Also, in BOC (Using Pythagoras)

$a^2 = h^2 + x^2$

Make $x^2$ the subject

$x^2 = a^2 - h^2$

Substitute $aSin\ C$ for h

$x^2 = a^2 - h^2$ becomes

$x^2 = a^2 - (aSin\ C)^2$

$x^2 = a^2 - a^2Sin^2\ C$

Factorize

$x^2 = a^2 (1 - Sin^2\ C)$

In trigonometry:

$Cos^2C = 1-Sin^2C$

So, we have that:

$x^2 = a^2 Cos^2\ C$

Take square roots of both sides

$x= aCos\ C$

In triangle BOA, applying Pythagoras theorem, we have that:

$AB^2 = h^2 + (b-x)^2$

Open bracket

$AB^2 = h^2 + b^2-2bx+x^2$

Substitute $x= aCos\ C$ and $h = aSin\ C$ in $AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2$

Open Bracket

$AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C$

Reorder

$AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C$

Factorize:

$AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C$

In trigonometry:

$Sin^2C + Cos^2 = 1$

So, we have that:

$AB^2 = a^2 * 1 + b^2-2abCos\ C$

$AB^2 = a^2 + b^2-2abCos\ C$

Take square roots of both sides

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

6 0

3 years ago

Roberto's toy car travels 600 inches at high speed and then another 456 inches at low speed. What is the total distance the car

Aleks04 [339]

600 + 456 = 1,056in

12 inches = 1 foot

1,056/12 = 88

The car would have travel 88 feet.

5 0

2 years ago

What is the area of 18 1/3 if the height of the window is 3 1/3

marin [14]

You would find the answer by dividing 3 1/3 from 18 1/3.
55/3 / 10/3
(55/3)(3/10)=55/10=5 1/2
Answer: 5 1/2

3 0

3 years ago

Label the quadrants IV

nevsk [136]

Answer:

Quadrant IV is always in the bottom right corner.

8 0

2 years ago

X2+ 1 = 9

Aleks04 [339]

Answer:

X = 4

Step-by-step explanation:

x2 + 1 = 9

We have to cross 1 over to the other side so that x becomes a value on its own. Because we are it over, the addition sign changes to subtraction which makes the expression,

x2 = 9- 1

x2 = 8

For x to stand alone we have to divide both sides by 2

x 2/2 = x

and 8/2 = 4

Therefore x=4 (Answer)

3 0

2 years ago