The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 degrees. The tree stands 20 ft off the hill. How high is the top of the tree from the base of the hill?
Answers
Answer:
Approximately [tex]101\; \rm ft[/tex] (assuming that the height of the base of the hill is the same as that of the observer.)
Step-by-step explanation:
Refer to the diagram attached.
Let [tex]\rm O[/tex] denote the observer.Let [tex]\rm A[/tex] denote the top of the tree.Let [tex]\rm R[/tex] denote the base of the tree.Let [tex]\rm B[/tex] denote the point where line [tex]\rm AR[/tex] (a vertical line) and the horizontal line going through [tex]\rm O[/tex] meets. [tex]\angle \rm B\hat{A}R = 90^\circ[/tex].Angles:
Angle of elevation of the base of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].Angle of elevation of the top of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].
Let the length of segment [tex]\rm BR[/tex] (vertical distance between the base of the tree and the base of the hill) be [tex]x\; \rm ft[/tex].
The question is asking for the length of segment [tex]\rm AB[/tex]. Notice that the length of this segment is [tex]\mathrm{AB} = (x + 20)\; \rm ft[/tex].
The length of segment [tex]\rm OB[/tex] could be represented in two ways:
In right triangle [tex]\rm \triangle OBR[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].In right triangle [tex]\rm \triangle OBA[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].For example, in right triangle [tex]\rm \triangle OBR[/tex], the length of the side opposite to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex] is segment [tex]\rm BR[/tex]. The length of that segment is [tex]x\; \rm ft[/tex].
[tex]\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}[/tex].
Rearrange to find an expression for the length of [tex]\rm OB[/tex] (in [tex]\rm ft[/tex]) in terms of [tex]x[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}[/tex].
Similarly, in right triangle [tex]\rm \triangle OBA[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}[/tex].
Equate the right-hand side of these two equations:
[tex]0.810\, x \approx 0.649\, (x + 20)[/tex].
Solve for [tex]x[/tex]:
[tex]x \approx 81\; \rm ft[/tex].
Hence, the height of the top of this tree relative to the base of the hill would be [tex](x + 20)\; {\rm ft}\approx 101\; \rm ft[/tex].
Related Questions
7/12 x 1/8 Find the product of in simplified form
Answers
Answer:
7/96
Step-by-step explanation:
to find the answer you need to multiply both numerators together and put that over the product of the denominators, this is going to leave you with a fraction smaller than the original fractions. that is normal, because you are multiplying terms smaller than one together. same applies to decimals less than one
a boy has 10 cookies. and his brother has 2.5 times as many. how many does the brother have
Answers
Answer:
25
Step-by-step explanation:
Find the equation for parabola
Focus(3,4)
Directrix y=2
Answers
Answer:
Step-by-step explanation:
we know that distance d from the focus to P should be the same to the distance from P to the directrix
(x-h)^2=4p(y-k)
we need to find the y coordinate,
x is the same from focus, 3
y=(3, (4+2)/2)=(3,3)
we find p now by subtracting the y from the focus from the y that we just found
p=4-3=1
again (x-h)^2=4p(y-k), p=1
(x-3)^2=4(1)(y-3)
(x-3)^2=4(y-3), (x-3)^2=4y-12
simplify
4y=(x-3)^2+12
y=((x-3)^2)/4 + 3
The equation for the parabola would be y = ((x-3)^2)/4 + 3.
How to find the equation for the parabola?We already know that distance d from the focus to P must be the same as the distance from P to the directrix
(x-h)^2 = 4p(y-k)
x is the same from focus 3
y = (3, (4+2)/2)
y =(3,3)
by subtracting the y from the focus from the y that we get
p = 4-3 =1
similalry,
(x-h)^2=4p(y-k), p=1
(x-3)^2=4(1)(y-3)
(x-3)^2=4(y-3),
(x-3)^2=4y-12
simplify it;
4y=(x-3)^2+12
y = ((x-3)^2)/4 + 3
Thus, the equation for the parabola would be y = ((x-3)^2)/4 + 3.
Learn more about parabola here;
https://brainly.com/question/16294220
#SPJ2
The right rectangular prism below has a square base?Select yes or no.
Answers
Answer:
no
Step-by-step explanation:
if it's a prism then it wont have a square bottom
Mr. Heath organizes a six-game tournament where players will
• earn 2.2 points for every game won (W),
• earn 1/4 point for any game ending in a tie (T), and
• lose 3 points for every game lost (L).
Tally a score for an imaginary player.
Make sure the player plays all six games and has at least one win, one loss, and one tie.
Write and solve an equation to find the player’s total score.
Answers
9514 1404 393
Answer:
(W, T, L, S) = (3, 2, 1, 4.1)
Step-by-step explanation:
For some number of wins (W), ties (T), and losses (L), the player's score will be ...
score = 2.2W +0.25T -3L
For 3 wins, 2 ties, and 1 loss, the player's score is ...
2.2(3) +0.25(2) -3(1) = 6.6 +0.5 -3 = 4.1
A box contains 1 3/4 Pasta how many ounces of pasta are in the box
Answers
Answer:
Step-by-step explanation:
is there more information to the question??
Which graph is defined by the function given below?
y= (x+3)(x +3)
-10
-10+
10-
A
B.
C
D.
Answers
Step-by-step explanation:
Since y = (x + 3)(x + 3), the root is x = -3.
Only Graph A touches the x-axis once.
WILL MARK BRAINLIEST PLEASE ANSWER 12/15+5/15 1 NUMBER FOR EACH SLOT
Answers
Answer:
17/15
Step-by-step explanation:
or if u reduce it would be 12/15
Your friend finds the measure of the exterior angle shown. Is your friend correct?
Answers
Answer:
will i think that's true
Step-by-step explanation:
I hope this helps you
Answer:
I think that it is yes
Step-by-step explanation:
Hope this helped have an amazing day!
Please help me slove this problem
3x - 3 = 12
Answers
Answer:
x=5
Step-by-step explanation:
We kind of have to work backward.
First, we take 12+3 because when we move it over the equal sign, we make it the opposite.
12+3=15
Our new equation is now, 3x=15
We now take:
3x__=15
The blank represents x, which is 5.
Hope this helps!
-AxekickNebulite
A farmer divided his piece of land into 2 equivalent groups and the quality of the soil is the same in both of these groups. He used fertilizers for the first group of land. He did not use fertilizers for the second group of land. At the end of the season, he measured the yield of the crops in these 2 groups. Is the study observational or experimental
Answers
Answer:
Observational would mean that he (farmer) has no direct impact or change on the statistical study.Experiment would mean that he imposed a certain treatment up a group in this case it would be the land.Hence we can determine that the the study was an experimental one.Many firms use on the job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performances of one of the trainees on the final test that was given to all trainees. The mean of the test score is 78. Additional information indicated that the median of the test scores was 85. What type of distribution most likely describes the shape of the test scores
Answers
Answer:
Skewed to the left
Step-by-step explanation:
In pearson mode skewdness, the mean, mode and median are used to determine if we have a positive or negative skewed distribution.
Now, If the mean is greater than the median, it means that the distribution is positively skewed and therefore skewed to the right. However, If the mean is less than the median, it means that the distribution is negatively skewed and therefore skewed to the left.
In our question, the median is 85 and mean is 78. Thus, it means median is greater than the mean and as such, the distribution isnegatively skewed and therefore skewed to the left.
4/5 times 1/5 PLZ ANSER I NEED HELP
Answers
Answer:
.16 or 4/25
Step-by-step explanation:
Answer:
4/25
Step-by-step explanation:
[tex]\frac{4}{5}[/tex]×[tex]\frac{1}{5}[/tex]
multiply tops together and denominators together and get [tex]\frac{4}{25}[/tex]
Which of the following is equal to 16.4 ?
O A. 32
O B. V16.4
O c.
D. 64
Answers
Answer:
b?
Step-by-step explanation:
b= v16.4
3. Determine whether the set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. 16, 30, 33
Answers
Answer:
all of them are acute
.......
Answer:
yes. it will be an acute.
1. The waiting times (in minutes) of customers at a certain bank is given below. 5.5 6.5 6.7 7.2 6.4 7.3 (a) Construct a 95% confidence interval for the mean waiting time of all customers at the bank. (b) Based on the confidence interval in (a), will the bank manager be satisfied if she wishes the average waiting time in her bank to be less than 7 minutes
Answers
Answer:
The 95% confidence interval is
[tex] 5.92 < \mu < 7.284 [/tex]
Step-by-step explanation:
From the question we are told that
The data is 6.5 6.7 7.2 6.4 7.3
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{\sum x }{n}[/tex]
=> [tex]\= x = \frac{ 5.5 + 6.5 + \cdot 7.3 }{ 6}[/tex]
=> [tex]\= x = 6.6[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \frac{ \sum (x_i - \= x )^2 }{ n-1} }[/tex]
=> [tex]\sigma = \sqrt{ \frac{ (5.5 - 6.6 )^2 +(6.5 - 6.6 )^2 + \cdot + (7.3 - 6.6 )^2 }{ 6-1} }[/tex]
=> [tex]\sigma = 0.6512[/tex]
Gnerally the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 6 -1[/tex]
=> [tex]df = 5[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]t_{\frac{\alpha }{2} , 5 } = 2.571 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2}, 5 } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.571 * \frac{0.6512}{\sqrt{6} }[/tex]
=> [tex]E = 0.6835 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]6.6 - 0.6835 < \mu < 6.6 + 0.6835[/tex]
=> [tex] 5.92 < \mu < 7.284 [/tex]
00:00
What is the number of terms in this expression?
m
5
+4x6
5
Enter your answer in the box.
Answers
Answer:
40
Step-by-step explanation:
Please solve this question.
Answers
Answer:
An equilateral triangle is formed.
Step-by-step explanation:
Since you construct two lines of 60° at points P and Q, the two ends of the line, you construct a triangle with two angles as 60°.
Hence, with the knowledge that the angle sum of a triangle is 180°, we can find that the remaining angle is [tex](180\textdegree - 60\textdegree - 60\textdegree)[/tex] = [tex]60\textdegree[/tex].
Therefore, a triangle with all angles at 60° is an equilateral triangle.
Hope this helped!
What is the value of x? enter your answer in the box.
Answers
Answer:
X = 20
Step-by-step explanation:
3x + 50 = 6x -10
3x - 6x = -10 - 50
-3x = -60
x = -60/-3
x = 20
Answer:
x = 20
Step-by-step explanation:
Vertically opposite angles are congruent.
6x - 10 = 3x + 50
6x = 3x + 50 + 10
6x = 3x + 60
6x - 3x = 60
3x = 60
x = 60/3
x = 20
Please help me thank you
Answers
Answer:
90
Step-by-step explanation:
90
The following list gives the number of siblings for each of 8 students. 3, 4, 2, 1, 2, 0, 3, 0 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."
Answers
Answer:
3, 2, 0
Step-by-step explanation:
There are three modes, all numbers have at least two appearances.
Please give thanks by clicking the heart! I solved your other problem too :)
Marita always listen to her favourite radio station when she drives her car
Everymoarning she listen to her radio
Answers
At ShopRite, chicken sells for $3.75 per pound. How much would it cost to buy 2.25 pounds of chicken?
Answers
Answer: 8.4375 U.S. dollars2
Step-by-step explanation:
Answer:
$8.44
Step-by-step explanation:
From the question it self we know that 1 pound of chicken costs $3.75. In order to solve this question we just need to find out how much 1 pound does fit into 2.25 pounds and then multiple the result by $3.75. We can find that out by dividing 2.25 by 1, and we get 2.25. Then we do the following....
2.25 x $3.75 = $8.4375
We got $8.4375 as an answer but we have to remember that when we are talking about money and we have to round to the nearest cent (which is equal to 1 hundredth of a dollar). So now we just have to round to the nearest hundredth, and we get $8.44 as our answer.
Which statement is true
A. The 6 in 0.6 is ten times the value of the 6 in 6.0 (wrong)
B. The 6 in 6.5 is 1/10 the value of the 6 in 65
C. The 6 in 625 is 100 times the value of the 6 in 625
Answers
Answer:
i think it A
Step-by-step explanation:
Solve y=3x-4 and y=2/5x+ 9
using systems of linear eqautions
Answers
Answer:
(5 , 11)
Step-by-step explanation:
[tex]Equation\ 1\\\\\y=3x-4\\\\Equation\ 2\\\\\y=\frac{2}{5}x+9[/tex]
There are three ways to solve the systems of linear equations
1) Elimination method - where we add/subtract the equations to eliminate the variable
2) Substitution method - where we substitute one variable in the form of another variable
3) Graphing method - where we sketch the graphs of both the equations and if they intersect that point would be the solution and if they don't there is no solution
We use the second method the Substitution method which is the easiest in my opinion.
Here we got two equations so lets just substitute equation 1 with equation 2 meaning insert equation 1 into equation 2 like here:
[tex]3x-4=\frac{2}{5}x+9[/tex]
as you can see here we eliminated the variable y by substituting y in terms of x.
Now we just solve the equation algebraically
[tex]3x-4=\frac{2}{5}x+9\\3x-\frac{2}{5}x=9+4\\\frac{15x-2x}{5} =13\\\\\frac{13x}{5}=13\\\\13x=65\\x=65/13\\x=5\\[/tex]
The value of x is 5 now to find the value of y we insert the value of x in any two equations lets insert the value of x into equation 1
[tex]y=3x-4\\y=3(5)-4\\y=15-4\\y=11[/tex]
so the solution of the system of linear equations is (5 , 11)
Kirby is packing granola bars for a filed trip. He already packed 2 bags with 5 granola bars in each bag. He has 10 more granola bars to pack. How many granola bars will Kirby pack in all
Answers
Answer:
20 granola bars
Step-by-step explanation:
Pls help I’m so confused! What would be the last step?
Answers
Answer:
SSS(Side,Side,Side)
Step-by-step explanation:
In the previous reasons you have proven that all of the sides of each triangle are equal to the corresponding side. You can use SSS to prove that the two triangles are congruent.
wirte the fractional coefficient for 1 1/4
Answers
One way to find the total cost of a jacket for $55 with a sales tax of 2%
Answers
Answer:
cost of jacket 55
sales tax 2/
55/ 2 percent × 100
2,750
i need help with this one (T_T)