Plz help, 20 points for a answer, plz help asap

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

A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.

IgorC [24]

Answer:

a = 2

Step-by-step explanation:

Let's find the equation of the line using the 2 points given.

Let's call -1 as x_1 and -5 as y_1

also, 4 as x_2 and 5 as y_2

The equation of line is :

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Let's plug the points and get the equation of the line:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y+5=\frac{5+5}{4+1}(x+1)\\y+5=2(x+1)\\y+5=2x+2\\y=2x-3$

Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:

$y=2x-3\\1=2(a)-3\\1=2a-3\\2a=4\\a=\frac{4}{2}=2$

4 0

3 years ago

Read 2 more answers

2.85 rounded to the nearest hundredth A. 2.861 B. 2.849 C. 2.842 D. 2.805

blagie [28]

Answer:

B) 2.849

Step-by-step explanation:

Given: 2.85 which is rounded to the nearest hundredth place.

To find the number, the thousandth place must be greater than or equal to 5.

Here 2.849 has the thousandth place greater than 5

When we round off 2.849 to the nearest hundredth place, we get

2.85

Therefore, answer is B) 2.849

Hope this will helpful.

Thank you.

5 0

3 years ago

Read 2 more answers

Plz help I will thank u and mark u as branilyest

IceJOKER [234]

number 9 =al you have to do is one and 7 eighths =9 so your sum will be 10 and 7 eighths.

hope this helps;)

MARK ME BRAINLIEST

YOU PROMISED!

8 0

3 years ago

Read 2 more answers

Let x be a Poisson random variable with μ = 9.5. Find the probabilities for x using the Poisson formula. (Round your answers to

miv72 [106K]

Answer: 1

Step-by-step explanation: the probability mass function that defines a possion probability distribution is given below as

P(x=r) = e^-u × u^x/x!

For this question, x = 0 and u = 9.5

Hence we have that

P(x=0) = e^-0 × 9.5^0 / 0!

P(x=0) = 1 × 1/ 1 = 1

5 0

3 years ago