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Answer:

Question 1)

[tex]\text{ Distance from A to the house is approximately 78.34 meters}\\\text{The height of the house is approximately 50.77 meters}[/tex]

Question 2)

[tex]\text{ Part A) \cos(x)=\frac{12}{13}} \\ \text{ Part B) \sin(90-x)=\frac{12}{13} }[/tex][tex]\text{ Part A) }\\\cos(x)=\frac{12}{13}\\\\\text{ Part B)}\\\sin(90-x)=\frac{12}{13}[/tex]

Step-by-step explanation:

Question 1)

Please first reference below for the image.

Also recall the basic trigonometric functions with SohCahToa.

Part 1)

In order to find the distance, we will need to find the value of [tex]x[/tex]. However, to do so, we must find the value of [tex]c[/tex] first.

First, we will need to find BM. We can use the smaller triangle. BM is opposite of the smaller triangle, and we already know that the hypotenuse is 20 meters. So, we can use sine:

[tex]\sin(A)=\frac{\text{opp}}{\text{hyp}}[/tex]

Substitute 32° for A and 20 for the hypotenuse. Our BM is our opposite, so substitute BM for opposite. This yields:

[tex]\sin(32)=\frac{BM}{20}[/tex]

Solve for BM. Multiply both sides by 20:

[tex]BM=20\sin(32)[/tex]

Don't approximate just yet. In order to make our answer to most precise, we will approximate at the very end.

So, BM is 20sin(32) meters. BM of the smaller triangle is the same as BM of the larger triangle, so BM of the larger triangle is also 20sin(32). Now, we can find the value of [tex]c[/tex]. However, we will first need to find the value of [tex]\angle MBT[/tex]. To do so, notice that [tex]\angle ABM, \angle MBT, \text{ and } 40\textdegree[/tex] form a straight angle. Therefore:

[tex]\angle ABM+\angle MBT+40^\circ=180[/tex]

Simplify:

[tex]\angle ABM+\angle MBT=140[/tex]

So, we will need to find [tex]\angle ABM[/tex], which is [tex]\angle B[/tex] of the smaller triangle. So, we can use the trig functions again. Since we now know BM, we can use cosine. So:

[tex]\cos(B)=\frac{\text{adj}}{\text{opp}}[/tex]

Substitute 20sin(32) for the adjacent and 20 for the opposite. So:

[tex]\cos(B)=\frac{20\sin(32)}{20}[/tex]

To solve for B, take the inverse cosine of both sides. Evaluate:

[tex]B=\cos^{-1}(\frac{20\sin(32)}{20})=58^\circ[/tex]

Therefore, we can substitute 58 for [tex]\angle ABM[/tex] and solve. This yields:

[tex]58+\angle MBT=140\\\Rightarrow\angle MBT=82^\circ[/tex]

So, we can now find c. We know BM and that [tex]\angle B[/tex] (of the larger triangle) is 82°. To find c, then, we will use cosine. So:

[tex]\cos(B)=\frac{\text{adj}}{\text{hyp}}[/tex]

Substitute 82 for B, 20sin(32) for the adjacent BM, and c for the hypotenuse. So:

[tex]\cos(82)=\frac{20\sin(32)}{c}[/tex]

Solve for c by cross-multiplying:

[tex]c=\frac{20\sin(32)}{\cos(82)}[/tex]

Now, finally, we can solve for [tex]x[/tex]. We know [tex]c[/tex] (the hypotenuse) and we want to find [tex]x[/tex]. We also have an angle of 40°. So, we can use cosine:

[tex]\cos(40)=\frac{x}{c}[/tex]

Multiply both sides by [tex]c[/tex]:

[tex]x=c\cos(40)[/tex]

Substitute [tex]c[/tex]:

[tex]x=\frac{20\sin(32)\cos(40)}{\cos(82)}[/tex]

Approximate:

[tex]x\approx58.34\text{ meters}[/tex]

However, this is only [tex]x[/tex]. The distance from the house is [tex]x+20[/tex]. Therefore, the distance from the house is:

[tex]d\approx58.34+20\approx78.34\text{ meters}[/tex]

Part 2)

We want to find the height h. Since we already determined [tex]c[/tex], we can use it to find [tex]h[/tex]. We will use the sine function this time:

[tex]\sin(40)=\frac{h}{c}\\\Rightarrow h=c\sin(40)\\\Rightarrow h=\frac{20\sin(32)\sin(40)}{\cos(82)}\\\Rightarrow h\approx48.95[/tex]

However, we will still need to add the eye level of 182 centimeters or 1.82 meters. So:

[tex]h\approx48.95+1.82\approx50.77\text{ meters}[/tex]

The height of the house is approximately 50.77 meters.

Question 2)

We know that: [tex]\tan(x)=\frac{5}{12}[/tex]

Remember that tangent is the opposite side over the adjacent side. So, let's find the hypotenuse. We can us the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute 5 for a and 12 for b. Solve for c:

[tex]c^2=(5)^2+(12)^2\\\Rightarrow c^2=25+144\\\Rightarrow c=\sqrt{169}=13[/tex]

So, our hypotenuse is 13, our adjacent is 12, and our opposite is 5. We can now solve for the others:

A)

[tex]\cos(x)=\frac{\text{adj}}{\text{hyp}}\\\Rightarrow\cos(x)=\frac{12}{13}[/tex]

B)

[tex]\sin(90-x)=\cos(x)\\\text{Note: This is a cofunction identity}\\\Rightarrow\sin(90-x)=\frac{12}{13}[/tex]

Note: The document I found said [tex]\sin^2(90-x)[/tex]. Anyways, it will just be: [tex]\sin^2(90-x)=\frac{144}{169}[/tex]

Answer:

105

Step-by-step explanation:

15/10= 1.5

30/20= 1.5

70x1.5= 105

Answer:

Step-by-step explanation:

There is no numeric answer, or there are many.

y = 7 - 2x is the first answer that you have to get.

Now you are away. The domain is anything.

The range (the y value) is also anything.

Answer:

-4y + 20x

Step-by-step explanation:

Answer:

x = 3, 7

Step-by-step explanation:

Step 1: Write equation

x² - 10x + 21 = 0

Step 2: Factor

(x - 7)(x - 3) = 0

Step 3: Find roots

x - 7 = 0

x = 7

x - 3 =0

x = 3

Answer:

green

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

5x + x = ?

5x + x = 6x

This is because x means 1x

Answer:

Today: Monday, 12 October 2020

Hour: 09.15 WIB (in Indonesian)

_________________________

5x + x =

x = 1

5x + x = 6x

Answer and explanation:

Find attached

Answer:

.19m+70=c

Step-by-step explanation:

.19m represents $0.19 per minute

+70 represents the fixed monthly fee

so you'd multiply the minutes by 19cents and add the $70 to find cost per month

9514 1404 393

Answer:

Step-by-step explanation:

The formula for slope (m) of a line between two points is ...

  m = (y2 -y1)/(x2 -x1)

Pick two points from the table and fill in the values. Using the last two table entries, we have ...

  m = (7 -5)/(5 -2) = 2/3

The slope is 2/3.

Answer:

5.5 years

Step-by-step explanation:

24900 times 6.75% = 1,680.75

so this is how much it goes down per year, but we have to find it were the price reaches 15900. so 9000-1680.75=

7,319.25( one year)

7,319.25-1680.75 = 5,638.5 (second year)

5,638.5-1680.75= 3,957.75 (third year)

3,957.75-1680.75 = 2,277 (fourth year)

2,277-1680.75= 596.25 (fifth year)

Answer:

the correct answer would be 5.5

Step-by-step explanation:

I solved it and got it correct on the test

Answer:

3.14 mph

Step-by-step explanation:

5.5 divided by 1.75

5.5 is the miles

1.75 is the hours

Answer: The average speed on the return trip is 2.44 miles/h

Step-by-step explanation:

Answer:  

5 and 11/50  

Step-by-step explanation:

5.22 = 261/50 = 5 and 11/50

Answer:99.9

Step-by-step explanation:

The percent of small businesses to all businesses is equal to 99.99%.

It is given that there are about 30.2 million small businesses and about 30000 large businesses.

We have to find out what percent of all businesses in the U.S. are small businesses.

What do you mean by percentage ?

A percentage is a number or say ratio that can be expressed as a fraction of 100.

As per the question ;

The approximate number of small businesses is ;

= 30.2 million

= 30200000

The number of large businesses is ;

= 30000

Total number of businesses will be ;

=  30200000 + 30000

= 30230000

The percent of small businesses to all businesses ;

= [tex]\frac{30200000}{30230000}[/tex] × 100 %

= 0.999 × 100 %

= 99.99 %

Thus , the percent of small businesses to all businesses is equal to 99.99%.

To learn more about percentage click here ;

https://brainly.com/question/18811795

#SPJ2

Answer:4

Step-by-step explanation:

Answer:

v: the answer is 43/48

Step-by-step explanation:

Answer:

If Eric sells boxes of cookies for $8 each, and Yolanda sells boxes of cookies for $10 each, and they made the same amount of money, then Eric sold 5 boxes.

Step-by-step explanation:

To solve this problem, you must find the lowest common multiple of eight and ten. That would be 40, which is how much they both made. $40 / $8 per box = 5 boxes.

...And you don't need to know this, but Yolanda sold 4.

Answer:

152%

Step-by-step explanation:

There is one whole grid shaded = 100%

The other grid has 13/25 shaded.  This is the same as 52/100=52%

100+52=152%

Answer: 152%

Step-by-step explanation: To easy please like

Answer:

m = 9

Step-by-step explanation:

m/4-3=9

m/(4-3)=9

m/1=9

m=9

Answer:

It would be positive, zero, negative, and undefined (the first answer).

Hope this helps!

[tex] \frac{5(q + p)}{2} = 3 + 4p \\ [/tex]

Multiply sides by 2

[tex]5(q + p) = 2(3 + 4p)[/tex]

[tex]5q + 5p= 6 + 8p[/tex]

Subtract sides minus 5p

[tex]5q = 6 + 8p - 5p[/tex]

[tex]5q = 3p + 6[/tex]

Divided sides by 5

[tex]q = \frac{3p + 6}{5} \\ [/tex]

a = 3 , b = 6 , c = 5

They're all positive.

So we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer:

the set of possible values of the independent variable or variables of a function.

Step-by-step explanation:

Answer:

All the x-values in the ordered pairs together make up the domain

Step-by-step explanation:

Thank you ☺️☺️

Answer: X=11

(2x+19)=(3x+8)

-2x -2x

19=(x+8)

-8 -8

11=x

Answer:

D

You use algebra and solve it for y.

Step-by-step explanation:

4x-3y=18

3y=4x+18

y=4/3x +6

Answer:

D

Step-by-step explanation:

Answer:

A. 1/3

Step-by-step explanation:

to find slope (rise over run), you count how many points up and how many points over it is to get from one point to another on the line graphed.

from point A to point B, it is 4 up and 12 over (4/12). then, you have to simplify it, making it 1/3.

hopefully that helped! please consider brainliest! :)

(I need one more to move up a rank lol)

Answer:

z=-3

Step-by-step explanation:

combine like terms then solve