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

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

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Answer: 21ft

Step-by-step explanation:

Answer:

the area of triangle is height ×base

6×7=42

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Answer:

x=4

Step-by-step explanation:

Power of the Point Theorem:

x*3=6*2

3x=12

x=4

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Sheryl earns about 13$ an hour so what you have to do is multiply 13 by 9 and then if I’m correct then that answer should land somewhere on the Line drawn

which method between graph method and table method friendly use? Motivate your answer​

Answers

Answer:

in my experience table method is friendly use because it is easier to work with than a graph

Graph is good for seeing the overall trend/pattern in your data

Table is good for knowing the specific numerics

Each has its pros and cons so use it based on your needs

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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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

hopefully this helps :)

have a nice day !!

A reflection is a flip over the

Y-axis

Line of reflection

X-axis

Answers

Answer

LINE OF REFLECTION

Step-by-step explanation:

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

which of the three curves drawn matches the graph of y = 2x 2 + x?

Answers

Answer:

y= 0 1 2 3 4

Step-by-step explanation:

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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

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]

Trig Ratios see attachment

Answers

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Step-by-step explanation:

Tangent is opposite/adjacent, so 5/12

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​

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Answers

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Answers

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Step-by-step explanation:

I hope this helps.

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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

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

Step-by-step explanation:

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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

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оооо
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Answers

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Answers

Answer:

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

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Answer:

Step-by-step explanation:

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Answers

the answer is the last option!!

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.

Hope this helps! :)

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