To calculate the height of a tree, Sophie measures the angle of elevation from a point “A” to be 34°. She then walks 10 m directly toward the tree, and finds the angle of elevation from the new point “B” to be 41°. What is the height of the tree, to the nearest tenth of a metre?
Answers
Answer:
30.1 Metres
Step-by-step explanation:
For this problem, we will use the law of sines twice to find the height of the tree.
First, you need to draw the image of the tree with two triangles, one with an angle of 34 degrees, and the second with an angle of 41 degrees, both being a right triangle toward the tree. The distance between point A and point B should be 10 meters.
From here, your bottom line of the triangle should be represented as 10 + x for the unknown distance from where Sophie stood to the tree. The x represents the distance from point B to the tree, whereas 10 + x represents the distance from point A to the tree.
Now, let's use the scalene triangle created by the distance between point A and point B to the top of the tree, to calculate the diagonal distance from point B to the top of the tree.
Using this scalene, we have the angles, 34, 7, and 139. Now, use the law of sines to find the diagonal of point B to the top of the tree represented by r.
sin(7) / 10 == sin (34) / r
r == 10 * sin (34) / sin(7)
r == 10 * .55919 / .12187
r == 45.88
Now that we know this diagonal distance, we can use the law of sines again with the second triangle, 41, 49, 90, to find the height of the tree represented by y.
sin(41) / y == sin(90) / 45.88
y == 45.88 * sin(41) / sin(90)
y == 45.88 * .65606 / 1
y == 30.1
So the height of the tree to the nearest tenth of a metre would be 30.1 metres.
Cheers.
Answer:
Hight of the tree: h = 30,1 mStep-by-step explanation:
tan(34°)≈0.6745 tg(41°)≈0.8693
[tex]\tan(34^o)=\dfrac h{x+10}\\\\\tan(34^o)(x+10)=h\\\\x+10=\dfrac h{\tan(34^o)}\\\\x=\dfrac h{\tan(34^o)}-10[/tex] [tex]\tan(41^o)=\dfrac hx\\\\x\tan(41^o)=h\\\\x=\dfrac h{\tan(41^o)}[/tex]
[tex]\dfrac h{\tan(34^o)}-10=\dfrac h{\tan(41^o)}\\\\ h\tan(41^o)-10\tan(34^o)\tan(41^o)=h\tan(34^o) \\\\ h\tan(41^o)-h\tan(34^o)=10\tan(34^o)\tan(41^o) \\\\ h[\tan(41^o)-\tan(34^o)]=10\tan(34^o)\tan(41^o)\\\\h=\dfrac{10\tan(34^o)\tan(41^o)}{\tan(41^o)-\tan(34^o)}\\\\\\h\approx \dfrac{10\cdot0.6745\cdot0.8693}{0.8693-0.6745}=\dfrac{5.8634285}{0.1948}\approx30.1\ m[/tex]
Related Questions
 I NEED HELP ASAP PLSS A regular hexagon has vertices at the coordinates listed below. Find the perimeter of the hexagon.
(-12, -8),(-12,7), (0,16),(12,7),(12, –8),(0, -17)
A. 90
B. 99
C. 114
D. 78
Answers
Answer:
B.99 its the answer....
Express the following in the usual form
(a) 6.25×10-⁵
Answers
Answer:
0.0000625
Step-by-step explanation:
[tex]10^{-5}=0.00001[/tex]
[tex]6.25*10^{-5}=6.25*0.00001=0.0000625[/tex]
Answer:
So we need to express [tex]6.25 * 10^{-5}[/tex].
What is being used here is scientific notation, and when the exponent is negative, that means the number is less than 1.
As the exponent is -5, we have to move the coma 5 positions to the left (if it was positive we would have done that put to the right), so:
[tex]6.25 * 10^{-5}=0.0000625[/tex]
If you don't understand what does it mean to move the coma to the left, see this example to understand it:
We move it one time from 6.25 --> 0.625
We move it two times from 6.25 --> 0.0625
We move it three times from 6.25 --> 0.00625
We move it four time from 6.25 --> 0.000625
What we are doing is adding 0 to the left and if the exponent was positive, we would add 0 to teh right.
So now we know that [tex]\boxed{6.25 * 10^{-5}=0.0000625}[/tex]
sixty nine no plz urgently
Answers
[tex]:\implies\sf\:\dfrac{4a^3}{a^4+x^4}+\dfrac{8a^7}{x^8-a^8}[/tex]
[tex]:\implies\sf\:\dfrac{4a^3(x^8-a^8)+8a^7(a^4+x^4)}{(a^4+x^4)(x^4-a^4)(x^4+a^4)}[/tex]
[tex]:\implies\sf\:\dfrac{4a^3x^8-4a^{11}+8a^{11}+8a^7x^4}{(a^4+x^4)^2(x^4-a^4)}[/tex]
[tex]:\implies\sf\:\dfrac{4a^3x^8+4a^{11}+8a^7x^4}{(a^4+x^4)^2(x^4-a^4)}[/tex]
[tex]:\implies\sf\:\dfrac{4a^3(a^8+2a^4x^4+x^8)}{(a^4+x^4)^2(x^4-a^4)}[/tex]
[tex]:\implies\sf\:\dfrac{4a^3\tt{(a^4+x^4)^2}}{{\tt(a^4+x^4)^2}(x^4-a^4)}[/tex]
[tex]:\implies\boxed{\bf{\purple{\dfrac{4a^3}{(x^4-a^4)}}}}[/tex]
What is the range of the function represented by the table?
Answers
Answer:
The second option
Step-by-step explanation:
the range is all the y vaules
Every month, Rachel gets a basic salary of $4000. He also get a bonus of $200 for each policy she sells and a bonus of $50 for each client’s complaint she resolves. Write an expression for her total salary for a month if she sells n policies and resolves x complaints.
Answers
Answer:
200n+50x+4000=Total Salary
Step-by-step explanation:
Let f(x) = - 3x – 1 and g(x) = x2 – 3.
Find (fog)(-7).
Then (fog)( - 7)= (Simplify your answer.)
Answers
Answer:-139
Step-by-step explanation:
f(x)= -3x-1
g(x)= x^2-3
(fog)(-7)=?
Soln'
fog(-7)
=f {(-7)^2-3}
=f (49-3)
=f (46)
=-3*46-1
=-139
13. In a cricket match, a batswoman hits a boundary 6times
out of 30 bells she plays. Find the probability that she plays .find the probability that she did not hit a boundary.
Answers
Answer:
4/5
Step-by-step explanation:
6/30 times she did
aka 1/5
5/5-1/5
=4/5 :)
Which of the following does NOT demonstrate a physical property of matter? A Salt and water combine to form a solution of salt water B Chocolate melts when it's left in the warm sun. C Batter changes to become cake when it is baked. D Water changes to water vapor when it reaches the boiling point
Answers
Answer:
b:chockelet
Step-by-step explanation:
TRUE OR FALSE QUESTIONS PLZ HELPPPP ME I BEG YOU:(((((((((((( pleaseee A story that is biased is slanted towards a particular point of view. True False The First Amendment protects freedom of speech. True False The federal government can influence state laws by withholding funding from states until they pass certain laws; for example, until they raise the legal drinking age to 21. True False When public opinion is led by public policy, the decisions or actions of political leaders influence the way people feel about certain situations. True False Republicans tend to favor more control by the federal government, while Democrats generally support more control by the people and states. True False People are more likely to vote in a close election. True False In a mayor-council system, a mayor serves as a city’s chief executive, while a city manager serves as the legislature. True False Local governments receive very little funding from state and local grants. True False
Answers
Answer:
True! i read the whole thing just for you, better thank me 5star review and brainliest
Step-by-step explanation:
how do you graph y= 6/5x + 1?
Answers
Answer:
Start at postive 1 on the y axis put a dot there. From the dot go down 6 and go left 5.
Step-by-step explanation:
6/5=rise over run
1=y-axis
y=mx+b
m=slope
b=y-intersept
Step-by-step explanation:
Hey, there!!
To graph a equation, we must find the coordinates of x and y.
So, as the equation is,
[tex]y = \frac{6}{5} x + 1[/tex]
Here, the equation is for finding the coordinates of y and x should be supposed. Remember, always suppose the value in equal interval.
Now,
x = 0 1 2 3
y= 1 2.2 3.4 4.6
Here, if you are confused how do i get 1, 2.2,3.4,4.6 as y value, put the value of x such as,
[tex]y = \frac{6}{5} \times 0 + 1[/tex]
which is equal to 1.
so,in this we got values.
Now,
List coordinates,
(0,1),(1,2.2),(2,3.4),(3,4.6)
Then plot on graph!!!
Hope it helps.....
A hot dog cart charges exactly $0.50 per hot dog. If the equation t=kh represents the total amount a customer is charged, t, for purchasing h hot dogs, what is the value of k?
Answers
Answer:
$0.50
Step-by-step explanation:
According to the information given, in the equation t=kh, t is the total amount a customer is charged and h is the amount of hot dogs purchased. So, to be able to get the total amount a customer is charged you have to multiply the amount of goods bought by the price of each good. Because of that, K would be the price per hot dog which is $0.50.
In the function f(x) = 4x -2, which of the following is the name of the function?
Answers
Answer:
The answer is "Linear function".
Step-by-step explanation:
Linear features would be those that have a linear graph. Its following location identified to a linear function, that is [tex]\bold{f(x) = a+bx}[/tex].
This function had a variable one of reliant to its variable, which is "x", and it's distinct and the response variable is reliant.
please find the attachment of the graph.
Find the equation of the hyperbola shown below. 15 Points, will give Brainliest! Due in 2 HOURS! A. (x - 1)^2/4 - (y + 4)^2/9 = 1 B. (y - 1)^2/4 + (x+4)^2/9=1 C. ( y + 1)^2/4 - (x - 4)^2/9 = 1 D. (y - 1)^2/9 - (x + 4)^2/4 = 1
Answers
Answer:
Solution:
[tex]\frac{\left(y-1\right)^2}{9}-\frac{\left(x+4\right)^2}{4}=1[/tex]
Step-by-step explanation:
We have the general equation for our up - down facing hyperbola as (y - k)² / b²- (x - h)² / a² = 1. Let's start listing the properties of this graph -
• Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1). Therefore (h, k) = (- 4,1).
• Another thing here is our key value a. This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference. Therefore a = 3.
• That leaves us with our asymptotes. Now remember that it will be in the form y = ± b / a. We already know a = 3, so we have to find b. Looking at this graph I can say that another point besides (- 4,1) that lies on the " dotted line " is (- 2, - 2). Calculating the slope of the dotted line would be as follows,
Given: (- 4,1) and (- 2, - 2)
Slope = - 2 + 4 / - 2 - 1 = 2 / 3
We have the equation y = 2 / 3x. Therefore b = 2. Let's substitute to receive our equation...
h = - 4, k = 1, b = 2, a = 3
(y - 1)² / (3)²- (x + 4)² / (2)² = 1
(y - 1)² / 9 - (x + 4)² / 4 = 1 ~ your solution is the last one, option d
Me palmo makes coffe at breakfast it takes the coffee maker 3 minutes to brew 24 cups of coffee at this rate how long will it take the coffee maker to brew 312 cups of coffee
Answers
because 312 divided by 24 equals 13 which is the number of times palmo makes coffee.
if you multiply 13 by 3 that gets you 39!
May you please with this questions
Answers
Answer:
m∠AED = 130°
Step-by-step explanation:
Definition of Supplementary Angles: 2 angles adjacent to each other that add up to 180°
Step 1: Define variables
m∠AEC = 50°
m∠AED = x (unknown)
Step 2: Set up equation
50 + x = 180
Step 3: Solve for x (subtract 50 on both sides)
x = 130°
Step 4: Replace variable x
m∠AED = 130°
Answer:130°
Step-by-step explanation: 50° is on a straight line. Therefore 180-50=130
Brad drives 527 miles on 17 gallons.How many miles does brad drive on one gallon? I know this is simple but i'm bad at math
Answers
If 140 students want to go on the Coronado Island field trip and are ALL riding together, how many cars will they need if each car holds 6 people?
Answers
Answer:
24
Step-by-step explanation
bruh...
1. Divide 140 by 6 and you get 23.3 repeating
2. When you multiply 23 times 6 you get 138. (not enough seats)
3. So, you would need to have at least 24 cars in order for everyone to go on the trip. (24 x 6 = 144 seats)
One of the angles of a right angled triangle is 52°. Find the other acute angle.
Answers
Answer:
Step-by-step explanation:
total angle of a triangle=180
52+90+x=180
x=180-(90+52)
x=180-142
x=38
Answer:
38
Step-by-step explanation:
Angle of a triangle is 180
52+90+x=180
x=180-(90+52)
x=180-142
x=38
Kerry has 77 dolls. Perry has e more dolls than Kerry. Write the expression that shows how
many dolls Perry has.
Answers
Answer: 77+e=Perry
Step-by-step explanation:
if you pulg in any number that is exacly what you will do to the number.
4 of 5
7 pens and 2 pencils costs £22.
3 pens and 4 pencils costs £11.
Find the cost of a pen.
Find the cost of a pencil.
pen: £
pencil: £
I
Answers
Answer:
pen: £3
pencil: £0.5
now I'm typing cause it said the answer needs to be at least twenty words long...
Which is the inverse function of y=3x-9
Answers
Answer:
y=1/3-3
Step-by-step explanation:
3.How will the number 847.89632 be written if rounded to the nearest hundredth?
Answers
Or you could write it as 847.9
What is the value of i5
1
−i
i
−1
Answers
If you did mean i^5, then the answer is i.
or to put it in simpler terms,
i^5=i
I hope this helped!
The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of the completely inflated balloon is 784π cm2, how long will it take for the balloon to fully inflate? Use SA=4πr2.
Answers
Answer:
7 seconds
Step-by-step explanation:
784 divided by 4 is 196
Square root of 196 is 14
2 cm per second
7 times 2 equals 14.
It will take 7 seconds for the balloon to fully inflate.
How to find time for the balloon to fully inflate?784 divided by 4 is 196
The square root of 196 is 14
2 cm per second
7 times 2 equals 14.
What is an example of a word problem?Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?
Learn more about Word problems here: brainly.com/question/13818690
#SPJ2
x+y/ 3 = 5 solve for x x+y is the numerator and 3 is denominator
Answers
Answer:
x=−y+15
Step-by-step explanation:
We’re five and twenty two hundredths centimeters as a decimal
Answers
Five and twenty-two hundredths centimeters as a decimal will be 5.22.
What are decimal values?A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole amounts.
Given, we need to find out the five and twenty-two hundredths centimeters as a decimal. Since five is a whole number so it will be 5 and twenty-two hundredths will be 0.22.
Therefore, 5.22 is the decimal value of the given question.
Learn more about decimals here:
https://brainly.com/question/29765582
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21 and 23 can best be described as -
Answers
Answer:
odd numbers
Step-by-step explanation:
you can see that end with odd numbers 1 and three so they can best be described as odd numbers
HOPE YOU FIND IT USEFUL
PLEASE HURRY WILL MARK BRAINLIST
what is the valuse of (-14^0)^-2?
-1/196
1/196
0
1
Answers
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1 and 1 to the power of anything is 1. In this case it is negative:
(-14^0)^-2
-1^-2
1
Select the correct answer Which is the correct simplified form of the expression (4m-2n^8)^1/2 ———— 9m^-6 n^-8
Answers
Answer:
[tex]= \frac{2m^2n^8}{3}[/tex]
Step-by-step explanation:
Given expression is
[tex](\frac{4m^{-2}n^8}{9m^{-6}n^{-8}} )^{\frac{1}{2}[/tex]
The correct simplified form is shown below:-
From the above equation, we will simplify
we will shift [tex]m^{-6}[/tex] to the numerator and we will use the negative exponent rule, that is
[tex]= (\frac{4m^{-2}n^8m^6}{9n^{-8}} )^{\frac{1}{2}[/tex]
now we will shift the [tex]n^{-8}[/tex] to the numerator and we will use the negative exponent rule, that is
[tex]= (\frac{4m^{-2}n^8m^6n^8}{9} )^{\frac{1}{2}[/tex]
here we will solve the above equation which is shown below
[tex]= (\frac{4m^4n^{16}}{9}) ^\frac{1}{2}[/tex]
So,
[tex]= (\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2} ^\frac{1}{2}[/tex]
Which gives result
[tex]= \frac{2m^2n^8}{3}[/tex]
What is the value of x
Answers
x equals negative 8 that's it
Answer:
-8
Step-by-step explanation:
3x+5-x=x-3
collect like terms
3x-x-x=-3-5
x=-8