Mathematics High School

Two forest rangers are standing on a road that runs east-west. One sights a forest fire in the direction 31° east of
north. The other sights the same fire 57° west of north.
Find the distance from each ranger to the forest fire and
the shortest distance from the fire to the road.

Two Forest Rangers Are Standing On A Road That Runs East-west. One Sights A Forest Fire In The Direction

Answers

Answer 1

Answer: The forest ranger closest to the fire is at a distance of 9.92 miles (nearest hundredth).

Draw a horizontal line AB of length 15 miles to represent the positions of the two forest rangers.

Point A is to the left and point B is to the right.

Complete triangle ABC so that m∠A = 41° and m∠B = 56°.

The point C represents the location of the fire.

Let x = length of BC. It is the shortest distance from the forest ranger B to the fire because BC is opposite the smaller angle of 41°.

Because the sum of angles in a triangle is 180°,

m∠C = 180° - (41° + 56°) = 83°.

From the Law of Sines,

x/sin(41) = 15/sin(83)

x = 15*[sin(41)/sin(83)] = 9.915 mi

Step-by-step explanation:

Draw a horizontal line AB of length 15 miles to represent the positions of the two forest rangers.

Point A is to the left and point B is to the right.

Complete triangle ABC so that m∠A = 41° and m∠B = 56°.

The point C represents the location of the fire.

Let x = length of BC. It is the shortest distance from the forest ranger B to the fire because BC is opposite the smaller angle of 41°.

Because the sum of angles in a triangle is 180°,

m∠C = 180° - (41° + 56°) = 83°.

From the Law of Sines,

x/sin(41) = 15/sin(83)

x = 15*[sin(41)/sin(83)] = 9.915 mi

Related Questions

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what’s the question

How many triangles can a polygon with 32 sides be sectioned into?

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32 sides of a polygon has 20 triangles.

Jerry rhombus has a base of 15 inches and a height of 9 inches. Charlene rhombus has a base

Answers

Complete Question:

Jerry’s rhombus has a base of 15 inches and a height of 9 inches. Charlene’s rhombus has a base and a height that are 13 the base and height of Jerry’s rhombus. Compare the area of Charlene’s rhombus to the area of Jerry’s rhombus.

Answer:

Charlene's rhombus has a larger area

Step-by-step explanation:

Given

Jerry's

[tex]Base = 15in[/tex]

[tex]Height = 9in[/tex]

Charlene's

[tex]Base = Height = 13in[/tex]

Required

Compare both areas

The area of rhombus is:

[tex]Area = Base * Height[/tex]

For Jerry's

[tex]Area = 15in * 9in[/tex]

[tex]Area = 135in^2[/tex]

Charlene's

[tex]Area = 13in * 13in[/tex]

[tex]Area = 169in^2[/tex]

By comparison: Charlene's rhombus has a larger area by 34in^2

Answer:

I THINK THE ANSWER IS 1/9 WHICH IS THE 2ND ANSWER.

Step-by-step explanation:

I DONT HAVE AN EXPLANATION BUT I DO KNOW ITS ACCURATE

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x^2-1

Step-by-step explanation:

I hope this helps.

What is the area of a triangle that has a height of 6 ft and a base length of 7 feet?

Answers

Answer: 21ft

Step-by-step explanation:

Answer:

the area of triangle is height ×base

6×7=42

i think this is the answer

A reflection is a flip over the

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Line of reflection

X-axis

Answers

Answer

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Step-by-step explanation:

In geometry, reflection basically just means flipping things over a line.

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Step-by-step explanation:

Solve x2 – 4х + 1 = 0.
x 2 + 215
оооо
х = 4 + 3
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Step-by-step explanation:

Trig Ratios see attachment

Answers

Answer:

TanA = 5/12, SinA = 5/13

Step-by-step explanation:

Tangent is opposite/adjacent, so 5/12

Sin is opposite/hypotenuse, so 5/13

Hopefully this helps! Let me know if you have any questions

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Answers

Answer:

x=4

Step-by-step explanation:

Power of the Point Theorem:

x*3=6*2

3x=12

x=4

Given the graph above, which equation could represent the function, given a > 1?

Answers

Answer:

Its B I am sure I have answered this and got it correct

Marcos makes a table to show how many students in his class wear glasses. There are 18 boys and 14 girls in the class. There are 5 boys and 7 girls who wear glasses. Which table correctly shows the data?

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Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Answer:

C. Y-6= 3/4 (x+4)

Step-by-step explanation:

two functions, A and B , are described as followed
​

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Answer:

it was never followed by the description

Step-by-step explanation:

A grocery store clerk put only packages of flour tortillas and packages of corn tortillas on the shelf. The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16.
Which number could be the number of packages of flour tortillas the clerk put on the shelf?

Answers

Answer:

32

Step-by-step explanation:

Answer: 18 and 32

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1. Anthony threw a ball from the top of a 10-story building that was 165 feet

tall. The equation g(165 - h) = v2 can be used to find the maximum

height the ball can attain after being thrown from the top of the building,

Rewrite the equation to highlight the maximum height attained by the

ball, h.

Answers

Answer:

[tex]h = 165 - \frac{v^2}{g}[/tex]

Step-by-step explanation:

Given

[tex]g(165 - h) = v^2[/tex]

Required

Make h the subject

[tex]g(165 - h) = v^2[/tex]

Divide both sides by g

[tex]165 - h = \frac{v^2}{g}[/tex]

Subtract 165 from both sides

[tex]165 - 165 - h = \frac{v^2}{g} - 165[/tex]

[tex]- h = \frac{v^2}{g} - 165[/tex]

Multiply both sides by -1

[tex]-1 * - h = (\frac{v^2}{g} - 165)*-1[/tex]

[tex]h = 165 - \frac{v^2}{g}[/tex]

PLEASE HELP!! DUE SOON

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Answers

Answer: Triangle 1

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Answers

Answer:

y-intercept: [tex](0,5)[/tex]

x-intercept: [tex](5/2,0)[/tex]

Answer:

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your gym membership cost $33 per month after an initial membership fee. you paid a total of $228 after 6 months. writer an equation that gives the cost as a function of the length of your gym membership (in months). find the total cost after 9 months

Answers

Answer:

what i did was multiply 33*6 and got 198 and then 228-198 to find out that the initial fee was 30 dollars. then multiply 33*9+30 to get a  9-month total cost of $327

Step-by-step explanation:

cost = $33 per month + fee  

1.  c(m) = 33m + f

 33(6) + f = 228

198 + f = 228

f = $30 membership fee  

c(m) = 33m + 30

 2.  at 9 months:  33(9) + 30 = $327

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Answer:

Reflection figure Q was flipped over the y-axis, the line of reflection.

Step-by-step explanation:

The figures have the same lengths but they are reflected.

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Step-by-step explanation:

:)

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Answers

Answer:

y= 0 1 2 3 4

Step-by-step explanation:

just minus 2 by all of the numbers from x

GH∥IK. Find GK. I need help with this please

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Answer:

Step-by-step explanation:

22

this is standard form (9x10 to the power of -4) to the power of 2

Answers

Answer:

9×10 to the power of -8

Step-by-step explanation:

Cause when we add power to the power we multiply them

For example [tex](2^{2} )^2[/tex] , we multiply the power so , 2×2= 4 so [tex](2^{2} )^2[/tex] = [tex]2^{4}[/tex]=16

Same here [tex]((9*10)^{-4} )^2[/tex] we multiply the powers so -4×2=-8

So [tex]((9*10)^{-4} )^2[/tex] =[tex](9*10)^{-8}[/tex] = 2.323×[tex]10^{-16}[/tex]

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Answers

Answer:

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At 100°F, a certain Insect chirps at a rate of 97 times per minute, and at 102°F, they chirp 111 times per minute. Write an equation in slope-intercept form that represents the situation.​

Answers

Answer:

y = 7x - 603

Step-by-step explanation:

We start by determining the slope:

m = y2 - y1/x2 - x1 = 111 - 97/102 - 100 = 14/2 = 7,

Now we substitute the slope into the slope-intercept equation y  = mx + b, solving for the y-intercept [b]:

111 = 7(102) + b,

b = -603

Equation: y = 7x - 603

What are the square roots of each perimeter of a rectangle?

Answers

Answer:

Step-by-step explanation:

The perimeter is simply 2 times length + 2 times width. In the case of our square, this would simply be 2x+2x (since length = width), or 4x . Therefore, if given an area, all you'd do is take the square root (to get from x2 to x , and then multiply by 4 to find perimeter.

Answer:

The first method

Take a square root, then multiply it by 4.

The defining characteristic of a square is that its length is equal to its width. Take a look below:

Self-created

So, for this particular square, the area is length⋅width, or x⋅x=x2. Now, how can you go from this to perimeter?

Well, the formula for perimeter is simply 2 times length + 2 times width. In the case of our square, this would simply be 2x+2x (since length = width), or 4x.

Therefore, if given an area, all you'd do is take the square root (to get from x2 to x, and then multiply by 4 to find perimeter.

The second method

s=√A

P=4×s

Explanation:

To find the perimeter of square, you just need to know the length of one side, because in a square all the sides are the same length.

If you know the area, find the square root of it to find the side.

s2=A

∴s=√A

Now you multiply by 4

For example, if the area is 36cm2

A=36

s=√36=6

P=4×6=24

Step-by-step explanation:

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