A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle of depression from where she is to the fire and finds it to be 34° How far away from the base of the tower is the fire?​

Answers

Answer 1

Answer:

[tex]103.78\:\mathrm{ft}[/tex]

Step-by-step explanation:

We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.

Therefore, we have:

[tex]\tan 34^{\circ}=\frac{70}{x}[/tex], where [tex]x[/tex] is the distance between the base of the tower and the fire.

Solving, we get:

[tex]x=\frac{70}{\tan 34^{\circ}}=103.779267796\approx \boxed{103.78\:\mathrm{ft}}[/tex]


Related Questions

Simplify r^2-2r^3+3r^2

Answers

Answer:

=−2r3+4r2

Step-by-step explanation:

r2−2r3+3r2

=r2+−2r3+3r2

=r2+−2r3+3r2

=(−2r3)+(r2+3r2)

=−2r3+4r2

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Write the equation of the line x 3y

Answers

Answer:

[tex]y = -3x + 14[/tex]

Step-by-step explanation:

Required

The equation of line

perpendicular to : [tex]x -3y =9[/tex]

Passes through [tex](3,5)[/tex]

We have:

[tex]x -3y =9[/tex]

Make y the subject

[tex]3y =x - 9[/tex]

Solve for y

[tex]y = \frac{x}{3} - 3[/tex]

Compare the above equation to [tex]y = mx + c[/tex]

[tex]m =\frac{1}{3}[/tex] ---- This represents the slope

Since the line is perpendicular to [tex]x -3y =9[/tex], then its slope is:

[tex]m_2 = -\frac{1}{m}[/tex]

[tex]m_2 = -\frac{1}{1/3}[/tex]

[tex]m_2 =-3[/tex]

The equation of the perpendicular line is:

[tex]y =m_2(x - x_1) + y_1[/tex]

Where:

[tex]m_2 =-3[/tex]

[tex](x_1,y_1) =[/tex] [tex](3,5)[/tex]

So:

[tex]y = -3(x - 3) + 5[/tex]

[tex]y = -3x + 9 + 5[/tex]

[tex]y = -3x + 14[/tex]

Ava read 121 books in 12.1 months. How many books per month did she read?

Answers

Answer:

10

Step-by-step explanation:

To find how many months, you need to divide by 12.1.

121/12.1 = 10

may u plz help me.....

Answers

Hundredths I think,,,,

Answer:

the 3 is in the hundredths place

Step-by-step explanation: the numbers from behind the decimals goes tenths, hundredths, thousandths. there is two spots behind making it hundredths  

I need help with this simple Geometry Question

Answers

Answer: 132º

Step-by-step explanation:

Since <QSR is an inscribed angle, that means that the intercepted arc, which is arc QR, is twice the measure of that angle, which is 132º. Since <QPR is a center angle, it is equal to its center arc. So, <QPR is 132º.

Really struggling, anyone mind explaining?

Answers

Step-by-step explanation:

You can solve this by splitting it into a net and calculating the areas of each shape

Count the triangles: 4

rectangles: 1

area of a triangle: 0.5 x b x h

area of a square : L x W

4(0.5 x b x h) + L x W = surface area

Suppose the following set of random numbers is being used to simulate the
event of a basketball player making five free throws in a row. How should the
numbers be rearranged?
860583 785814 010122 337198 621549 034076 796495 978078 433330
333153
A. 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978
078 433 330 333 153
B. 8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597
8078 4333 3033 3153
C. 86058 37858 14010 12233 71986 21549 03407 67964 95978
07843 33303 33153
D. 860583 785814 010122 337198 621549 034076 796495 978078
433330 333153

Answers

The list that represents the simulation of five free throws is (c) 86058 37858 14010 12233 71986 21549 03407 67964 95978 07843 33303 33153

To illustrate the simulation of five free throws, then each number on the list must have 5 digits

The list is given as:

860583 785814 010122 337198 621549 034076 796495 978078 433330 333153

When rearranged, we have:

86058 37858 14010 12233 71986 21549 03407 67964 95978 07843 33303 33153

Hence, the list that represents the simulation of five free throws is (c) 86058 37858 14010 12233 71986 21549 03407 67964 95978 07843 33303 33153

Read more about random numbers at:

https://brainly.com/question/251701

I need the answer to this question

Answers

Answer:

Option(A)

Step-by-step explanation:

y=4x+2

When you replace the value of x in the equation you get the value of y

Answer:

the answer is A since if we lay it out we will get y

-6=-2*4+2

2=0*4+2

6=1*4+2

find the missing angles

Answers

[tex]\huge\bold{Given :}[/tex]

Angle a = 39°

Angle c = 123°

[tex]\huge\bold{To\:find :}[/tex]

The measure of angle b.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

∠ b = 18°

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

We know that,

[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]

➪ ∠ a + ∠ b + ∠ c = 180°

➪ 39° + ∠ b + 123° = 180°

➪ ∠ b + 162° = 180°

➪ ∠ b = 180° - 162°

➪ ∠ b = 18°

Therefore, the measure of ∠ b is 18°.

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

∠ a + ∠ b + ∠ c = 180°

✒ 39° + 18° + 123° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

[tex]\boxed{Hence\:verified.}[/tex]

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

please help ASAP (math)

Answers

i believe its the third one, because you just plug in the values to the vertex form

Can u help me with this?

Answers

Answer:

b

Step-by-step explanation:

it is the right answer pls believe me

if 1/3 of a number is added to 1/5 of the same number.the result is 8. find the nnumbe

Answers

Answer:

15

Step-by-step explanation:

the number is 15 as solved or proved in the figure above

1. Of the three angles in a right-angled triangle, one angle has a measure
of 60 degrees. What is the measure of the third angle, Angle X? *
al 60

Answers

Answer:

30°

Step-by-step explanation:

180 - 90 - 60 = 30

Can someone please help me? You get points and it makes me happy.

Melanie makes $3.00 less per hour babysitting than her best friend, Carita. If the combined hourly rate of Melanie and Carita is $15.00, how much does Melanie make per hour?
A. $3.00
B. $6.00
C. $9.00
D. $12.00


No links or fake answers pls. Thanks for understanding.

Answers

The answer is C. $9.00

Answer:

$6

Step-by-step explanation:

(x-3)+x=15

2x-3=15

2x=18

x=9

9-3=6

Melanie makes 6 and Carlita makes 9.

Roger and Rita each drive at a constant speed between Phoenix and San Diego. Each driver’s distance for the same section of the trip is displayed below.

Who had a head start, and how many miles was the head start?

Answers

Answer:

The one you chose in the image is correct (A)

Answer:

a: Rita had a 28 mile head start

Step-by-step explanation:

Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
14x^4y^6/7x^8y^2
A. 2y^4/x^3
B. 7y^3/x^2
C. 7x^4y^4
D. 2x^2y^3

Answers

Answer:

The answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope this Helps ;)

What is the equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15

Answers

9514 1404 393

Answer:

  x + 3y = 9

Step-by-step explanation:

The parallel line will have the same x- and y-coefficients. The new constant can be found by using the (x, y) values of the given point.

  x + 3y = (6 +3(1)) = 9

The equation of the parallel line is ...

  x + 3y = 9

PLEASE PLEASE HELP ME

Answers

Sum of angle in a triangle is 180, so 33+70+x=180
x=77
x and y are vertical angles so y=77

Answer:

x = 77

Step-by-step explanation:

All angles in a triangle equal to: 180

70 + 33 = 103

180 - 103 = 77

Have a nice day!

Which of the following is equivalent to log50^7 rounded to three decimal places

Answers

Answer:

11.886

Step-by-step explanation:

Given :

[tex]log 50^7[/tex]

Applying formula

[tex]log a^m=m log a[/tex]

So,

[tex]7 log 50\\=7(1.698)\\=11.886[/tex]

Answer will be 11.886

Pleas help y’all please

Answers

Answer:

option 3

Step-by-step explanation:

BODMAS : the expression contains addition and division. So we will do division first and then addition.

[tex]\frac{1}{3} + \frac{5}{4} \div \frac{3}{2}\\\\\frac{1}{3} + (\frac{5}{4} \div \frac{3}{2})\\\\\frac{1}{3} +( \frac{5}{4} \times \frac{2}{3} )\\\\\frac{1}{3} + \frac{5}{6}\\\\\frac{2 + 5}{6} \\\\\frac{7}{6} = 1 \frac{1}{6}[/tex]

A cylinder has a volume of 187 cubic inches. If the radius is 3 inches, what is the height of the cylinder in inches?

Someone please help

Answers

Answer:

Step-by-step explanation:

V = pi r^2 h

V = 187

pi = 3.14

r = 3

h = ?

187 = 3.14 * 3^2 * h

187 = 3.14 * 9 * h

187 = 28.26 * h

187 / 28.26 = h

h = 6.62

Answer:

The height of cylinder is 6.61 inches.

Step-by-step explanation:

Given that :- Volume of cylinder = 187 inches ³.Radius of cylinder, r = 3 inches

We need to Find :-Height of cylinder , h

Formula Used :-

Volume of cylinder = π × r ² × h

Where,

r is the radius of cylinder. h is the height of cylinder.

Solution :-

Using Formula

Volume of cylinder = π × r ² × h

Substitute the values

187 inches ³ = π × ( 3 inches ) ² × h

Using π = 3.14

187 inches ³ = 3.14 × 9 inches ² × h

multiply

187 inches ³ = 28.26 inches ² × h

Divide , we get

187 inches ³ / 28.26 = h

6.61 inches = h

Therefore, The height of cylinder is 6.61 inches.

HELPPP EDCITEEE !!!!!!!!!!!!!!!!!!!!!

Answers

105.6yds2

Explanation:
The formula for area of triangle is:
1/2 • base • height
In this case, it is:
1/2 • 17.6 yd • 12 yd
= 105.6 yds2

MARK ME BRAINLIEST TYSM!
yup what the other person said

what is the algebraic expression of 3 divided by q please answer grade 6 way

Answers

Answer: 3/q

Step-by-step explanation:

The answer to the question is 3/q

If a seed is planted, it has a 90% chance of growing into a healthy plant. If 10 seeds are planted, what is the probability that exactly 2 don't grow

Answers

The probability that exactly 2 seeds will don't grow will be equal to 0.193.

What is Probability?

Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.

As per the given information in the question,

P(2 don't grow) = P(8 will grow)

Use the formula given below,

P(X = r) = [tex]^nC_r\ p^r(1-p)^{n - r}\\[/tex]

P(X = 8) = ¹⁰C₂ (0.9)⁸(0.1)²

= 45 × 0.43 × 0.01

= 0.193

To know more about Probability:

https://brainly.in/question/54143022

#SPJ5

What is the value of the expression shown below? ​

Answers

Answer:

11 1/8

Step-by-step explanation:

(I think u did the PEMDAS wrong)

10 + ( 36) / 4 x 1/8

36 / 4 = 9

9 x 1/8 = 9/8

10 + 9/8 = 89/8

89/8 = 11 1/8

Answer:

1st one

Step-by-step explanation:

Richard and Braden are playing a game with a pair of dice. Richard needs a sum greater than 9 to win. What is his probability of winning on his next turn?

Answers

Answer:

5/12

Step-by-step explanation:

Notice that the in the throw of a pair of dice.

Sum               No. of times Favorable outcome

8                                 5

9                                  4

10                                 3

11                                  2

12                                 1

And total otcome = 6×6 =36

There P ( richard win) = P(X≥8)

=  (5+4+3+2+1)/36

=5/12

The equation is y = -5(3^x)

Answers

Answer:

C

Step-by-step explanation:

Since the number outside of the parentheses is -5, the negative factor means that the line is reflected across the x-axis.

the answer is C!
hope that helps, i’m pretty sure it’s right

PLZ HELLPPP!!!I would really apreciate it 25 POINTS!!!

Answers

you take the amount of days and multiply by 50! so if the days are d, and cost is c then c=50d
hope this helps, can i have brainliest!

The position of an atom moving inside a cathode ray tube is given by the function f(t) = t^3− 4t^2 + 3t where t is in seconds and f(t) is in meters. Find the instantaneous velocity of the atom at t = 2.5 seconds. A. 1.75 m/sec. B. 2.48 m/sec. C. 3.27 m/sec. D. 4.12 m/sec.

Answers

Answer:

A

Step-by-step explanation:

The position of an atom moving inside a cathode ray tube is given by the function:

[tex]f(t)=t^3-4t^2+3t[/tex]

Where f(t) is in meters and t is in seconds.

And we want to determine its instantaneous velocity at t = 2.5 seconds.

The velocity function is the derivative of the position function. Thus, find the derivative of the function:

[tex]f'(t)=3t^2-8t+3[/tex]

Then the instantaneous velocity at t = 2.5 will be:

[tex]f'(2.5)=3(2.5)^2-8(2.5)+3=1.75\text{ m/sec}[/tex]

Our answer is A.

Answer:

Instantaneous Velocity:

[tex]\longrightarrow\:\rm v = \dfrac{dt}{dy}[/tex]

[tex]\longrightarrow\:\rm v = \dfrac{d}{dy}( {t}^{3} - 4 {t}^{2} + 3t) \\ [/tex]

[tex]\longrightarrow\:\rm v = 3 {t}^{3 - 1} - 2.4 {t}^{2 - 1} + 3[/tex]

[tex]\longrightarrow\:\rm v = 3 {t}^{2} - 8 t + 3[/tex]

[tex]\longrightarrow\:\rm v = 3 {(2.5)}^{2} - 8 (2.5)+ 3[/tex]

[tex]\longrightarrow\:\rm v = 3 \times 6.25 - 20+ 3[/tex]

[tex]\longrightarrow\:\rm v = 18.75 - 20+ 3[/tex]

[tex]\longrightarrow\:\rm v = 18.75 - 20+ 3[/tex]

[tex]\longrightarrow\:\bf v = 1.75 \: {ms}^{ - 1} [/tex]

find the solution to 8x^2 + 56x=0

Answers

Answer:

[tex]x = 0, - 7[/tex]

Step-by-step explanation:

[tex]8x^2 + 56x=0[/tex]

[tex]8x(x)+56x=0[/tex]

[tex]8x(x)+8x(7)=0[/tex]

[tex]8x(x+7)=0[/tex]

[tex]x=0 [/tex]

[tex]x+7=0[/tex]

[tex]x=−7[/tex]

Hope it is helpful...
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