3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can view both cars. One car can be viewed at an angle of depression of 370, and the other car can be viewed at an angle of depression of 420. How tall is the building?
Answers
Answer:
The building is 61.5 m tall
Step-by-step explanation:
The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:
h = height of the building
a, b = internal angles of each triangle
x = base of each triangle
The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:
a = 90° - 37° = 53°
b = 90° - 42° = 48°
Now we apply the tangent ratio on both triangles separately:
[tex]\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 53^\circ=\frac{150-x}{h}[/tex]
[tex]\displaystyle \tan 48^\circ=\frac{x}{h}[/tex]
From the last equation:
[tex]x=h.\tan 48^\circ[/tex]
Substituting into the first equation:
[tex]\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}[/tex]
Operating on the right side:
[tex]\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ[/tex]
Rearranging:
[tex]\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}[/tex]
Solving for h:
[tex]\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}[/tex]
Calculating:
h = 61.5 m
The building is 61.5 m tall
Related Questions
A student club has 20 members how many ways are there for the club to choose a president and a Vice President
Answers
Answer:
Everyone should get president every month simple
A baseball player batted 544 times in a season, with a batting average of 0.294. Using the formula below, find the number of hits he made.
The batting average formula is a=h/n where a is the batting average, h is the number of hits, and n is the number of times at bat.
Answers
Answer:
Calculate Batting Average
Calculating a baseball player's batting average is not a difficult task at all. A batting average represents the percentage of at bats that result in hits for a particular baseball player. The formula is:
Hits / At Bats = Batting Avg.
That's all there is to it. For example, if Justin Upton gets 155 hits in a season and has 554 at bats, his batting average would be 155/554, or .280. The batting average is usually represented not as a percentage (i.e. 28.0%), but instead as a decimal number with three places after the decimal. A batting average of 1.000 means that the player gets a hit every time he comes to bat, and an average of .000 means the player has no hits.
It should also be noted that not every time a batter comes to the plate counts as an at bat. Plate appearances that do not count as at bats include walks, hit-by-pitches, sacrifices, etc.
Here's one last example: Albert Pujols gets 35 hits in 113 at bats in May, so his batting average would be calculated as 35 divided by 113, which is .310 for the month of May.
Step-by-step explanation:
Answer:
160
Step-by-step explanation:
The previous answer response to this question was too long and complicated. Just follow the things you know from the question and use the formula.
a=h/n, a is the batting average, h is the number of hits, and n is the number of times at bat. Use substitution to make your formula now look like this:
0.294 = h/544.
Now you have to get h by itself. To do that, you do the opposite of division: multiply. What you do to one side, you do to the other.
544(0.294 = h/544)544 ⇒ h = 544 x 0.294.
Your result should be 159.936; round to the nearest whole number ⇒ 160.
A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). The regression output is provided below. Some of the information has been omitted.Sources of variation SS df MS FRegression 3177.17 2 1588.584 Residual 17 17.71713 Total 3478.36 19 How many predictors (independent variables)were used in the regression?
A) 20
B) 18
C) 3
D) 2
Answers
Answer: B) 18
Step-by-step explanation: It is also widely used for predicting the value of one dependent variable from the values of two or more independent variables. When there are two or more independent variables, it is called multiple regression
The number of independent variables or predictors present in the regression model is 3.
The number of independent variables can be obtained from an ANOVA table of the degree of freedom column of corresponding to RegressionThe Regression degree of Freedom usually denoted as k - 1 ; where k is the number of independent variables. From the ANOVA table given ; k - 1 = 2 The value of k = 2 + 1 = 3 ; Therefore, the value of k in the regression table is 3.Therefore, the number of predictors in the regression is 3.
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What is the quotient of 4/5 divided by 17/9
Answers
Answer:
0.42352941176
Step-by-step explanation:
hope this helps
The value of quotient will be 0.42.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
''4/5 divided by 17/9''
Now,
Since, The expression is,
''4/5 divided by 17/9''
Hence, After solving we get;
⇒ 4/5 ÷ 17/9
⇒ 4/5 × 9/17
⇒ 36/85
⇒ 0.42
Thus, The value of quotient = 0.42
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If sinA 3/5 and cos B 5/13 , then find the value of sin (A+B)
Answers
Answer:
[tex] \frac{63}{65} [/tex]
Step-by-step explanation:
We have to find the value of sinB & cosA . So to find the value of sinB , let's use the identity
[tex] { \sin }^{2} b + { \cos }^{2} b = 1[/tex]
By using the identity above gives
[tex] { \sin}^{2} b + ( { \frac{5 }{13} })^{2} = 1[/tex]
[tex] = > { \sin}^{2} b = 1 - \frac{25}{169} = \frac{144}{169} [/tex]
[tex] = > \sin(b) = \sqrt{ \frac{144}{169} } = \frac{12}{13} [/tex]
Now to find the value of cosA , we'll use the same identity.
[tex] {( \frac{3}{5} })^{2} + { \cos}^{2} a = 1[/tex]
[tex] = > { \cos }^{2} a = 1 - \frac{9}{25} = \frac{16}{25} [/tex]
[tex] = > \cos(a) = \sqrt{ \frac{16}{25} } = \frac{4}{5} [/tex]
Now we know that
[tex] \sin(a + b)=\sin(a)\cos(b)+\sin(b) \cos(a) [/tex]
So value of sin(a+b) =
[tex] \frac{3}{5} \times \frac{5}{13} + \frac{12}{13} \times \frac{4}{5} [/tex]
[tex] = \frac{3}{13} + \frac{48}{65} [/tex]
[tex] = \frac{63}{65} [/tex]
The graph of an equation shown below: based on the graph, which of the following represents the solution to the equation? (-2, -3) (2, 1) (1, 2) (-3, -2)
Answers
4 (3u - 1) - 4u = 76*
u=?
Answers
Answer: 12u-4-4u=76
Step-by-step explanation: Use distributive property and PEMDAS, that might help.
ABCD is a square.
Solve for x
Answers
Hope you have a good day and good luck!
An oxygen mask is placed on a patient. Oxygen is administered to the patient for 5 minutes. Then the oxygen
mask is removed and the amount of oxgyen in the body decreases exponentially. Which graph best describes the
amount of oxygen in the patient's bloodstream beginning with the moment when oxygen is first administered?
Answers
HELP ME PLEASE !!! please
Answers
Answer:
(0,0) and (60,0)
Step-by-step explanation:
because they are the points on the x-axis
The question is below
Answers
9514 1404 393
Answer:
162°
Step-by-step explanation:
The measure of inscribed angle ADC is half the measure of the intercepted arc AC. That arc has a measure that is the same as the central angle it subtends, angle ABC.
So, central angle ABC is twice the measure of inscribed angle ADC:
m∠ABC = 2·81° = 162°
Lines a, b, c, and d are distinct lines in the same plane. Decide if lines a and d are parallel, perpendicular, or if there is not enough information
Answers
Answer:
A. Parrellel
Step-by-step explanation:
it is parrellel because if you look between b and c you can
see that it is a parrellel line
how are <1 and <2 related
Answers
Answer:
They are adjacent
Step-by-step explanation:
how many half's are in a whole
Answers
1/2 plus 1/2 = 1
Hope this helps and have a nice day!!!
(If it is right don’t forget to mark branliest :) )
Answer:
Two
Step-by-step explanation:
Because 1/2 plus 1/2 equals 1 witch would be the final half to make one whole
Difference in Roth IRA and Traditional IRAs, pension plans, 401Ks
Answers
Answer:
Contributions to a 401(k) are pre-tax, meaning they are deposited before your income taxes are deducted from your paycheck. However, when in retirement, withdrawals are taxed at your then-current income tax rate. Conversely, there is no tax savings or deduction for contributions to a Roth IRA
Can someone help with this please? I think it has to do with the Pythagorean theorem.
Answers
Answer:
2 sqrt(13)
Step-by-step explanation:
We can use the Pythagorean theorem
The x value between A and B is 4 units and the y value is 6 units
The distance is
d = sqrt( x^2 + y^2)
= sqrt( 4^2 + 6^2)
= sqrt( 16+36)
= sqrt(52)
= sqrt(4*13)
= 2 sqrt(13)
Write an equivalent expression. 2 + 4(c + 7)
A) 4c + 9
B) 30 + 4c
C) 6c + 9
D) 15 + 4c
Answers
2 + 4c + 28
combine liked terms
4c + 30
Answer:
B) 30 + 4c
If two rectangles are similar, what is the length of side x? Give your answer to one decimal place. Rectangle 1: A = 13.4ft B = 4.6ft Rectangle 2: A = 87.1 ft B = x
Answers
Answer:
x = 29.9 ft
Step-by-step explanation:
Given:
Rectangle 1 ≈ Rectangle 2
In Rectangle 1
A = 13.4 ft
B = 4.6 ft
In Rectangle 1
A = 87.1 ft
B = x ft
Find:
Value of x
Computation:
Rectangle 1 ≈ Rectangle 2
So,
13.4 / 4.6 = 87.1 / x
x = [(87.1)(4.6)] / 13.4
x = 29.9 ft
I AM IN A TEST AND I NEED THE ANSWER SOON!!! PLEASEE!!!
THANK YOU SO MUCH!!
Answers
If Viviana has 2/5 of pasta to share with four friends, you should divide. First change 2/5 to a decimal, 0.4. Now divide 0.4 and 4.
Workspace:
2/5 = 0.4
4 / 0.4 -> 10
Workspace End
Correct Answer:
10
Hope this helps!!
Brainliest??
How many adults visited the museum in February
Answers
Answer:
83 adults visited the museum on february...
Step-by-step explanation:
hope this helps
f(x + 1) = 2x + 1
g(x + 1) = x-5
> (fog)(2) = ?
Answers
Solve:
-3(1 + 4x) = 33
x =
Solve:
-4(-6y – 3) = 12
y =
Solve:
-(x – 8) = -2
x =
Solve:
−3(4r − 8) = −36
r =
Solve:
6(−x − 3) = 24
x =
Solve:
3(x − 2) = 18
x =
Solve:
2(4x + 4) = 24
x =
Please help
Answers
Answer:
−
3
(
1
+
4
)
=
3
3
Step-by-step explanation:
Answer:
1: -3
2: 24
3: 10
4: 5
5: -7
6: 8
7: 2
Step-by-step explanation:
hope this helps:)
a farmer grows 128 red tomato plants and 102 yellow tomato plants each plant produces about 32 tomatoes the farmer plans to sell each tomato for$2
Answers
Answer:
14720$ he will make and there are 7360 tomatoes
Step-by-step explanation:
The ratio of boys to girls on Rowan’s swim team is 2:3. If there are 24 boys on the team, how many girls are there?
Answers
Answer:
36 girls
Step-by-step explanation:
2x=24
x=12
3(12) = y
y= 36
graph the image of triangle UVW after a reflection across the line x = -1
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Reflection over the line x = -1 alters the x-coordinates, but leaves the y-coordinates alone. The image point is as far horizontally from the reflection line as the pre-image point is.
Each new x-coordinate is the old one subtracted from twice the x-value of the line of reflection:
(x, y) ⇒ (-2-x, y)
U(-8, -6) ⇒ U'(6, -6)
V(-3, -6) ⇒ V'(1, -6)
W(-4, -1) ⇒ W'(2, -1)
Please help me solve this question will give you braisnlt !
Answers
Answer:
[tex]s = 54m +160[/tex]
Step-by-step explanation:
Given: The attachment
Required: Determine the equation
We start by picking any two equivalent points on the table:
[tex](m_1,s_1) = (2,268)[/tex]
[tex](m_2,s_2) = (4,376)[/tex]
Next, we determine the slope, M:
[tex]M = \frac{s_2 - s_1}{m_2 - m_1}[/tex]
[tex]M = \frac{376 - 268}{4-2}[/tex]
[tex]M = \frac{108}{2}[/tex]
[tex]M = 54[/tex]
The equation is then calculated as:
[tex]s - s_1 = M(m - m_1)[/tex]
Where:
[tex]M = 54[/tex]
[tex](m_1,s_1) = (2,268)[/tex]
So, we have:
[tex]s - 268 = 54(m - 2)[/tex]
Open bracket
[tex]s - 268 = 54m - 108[/tex]
Collect like terms
[tex]s = 54m - 108 + 268[/tex]
[tex]s = 54m +160[/tex]
Hence, the equation is: [tex]s = 54m +160[/tex]
Question in picture below will give brainly
Answers
Answer:
only student ll (2)
Step-by-step explanation:
A bowling alley charges a one-time fee of $5.50 to rent shoes and $3.50 per game. Write an equation that represents "y", the total dollar amount that you must pay to bowl "x" games.
Please help this is due today, I would appreciate it if you did help!
Answers
Answer: 14$
Step-by-step explanation:
let x = number of games, let y = cost of shoe rental
then Total cost = x•$4 + y
In this case, TC = 3•$4 + $2
TC = $14
A local grocery store decides to offer a free piece of fresh fruit (banana or apple) to all shoppers in the produce department. The store is conducting an observational study to determine which type of fruit is selected more often. At the end of the first day, the store found that twice as many shoppers select an apple.
The grocery store then repeats the observational study for 14 days. All studies yield similar results. What generalization can be made from the results of this study?
A.
Given the choice of a banana or an apple, twice as many shoppers will select an apple.
B.
The results are inconclusive; therefore, a generalization cannot be made regarding which type of fruit is preferred by most shoppers.
C.
There is not enough information to generalize the study’s results.
D.
Given the choice of any type of fruit, twice as many shoppers will select an apple.
Answers
Answer:
A.
Step-by-step explanation:
If the results are similar (A) should be your answer!
Option A is correct.
What is generalization?Generalization is a process which leads to something more general and whose product consequently refers refers to an actual or potential manifold in a certain way.
According to the given question
"At the end of the first day, the store found that twice as many shoppers select an apple"
So, the generalization can be made from the above result is " from the given choice of a banana or an apple, twice as many shoppers will select an apple".
Hence, option A is correct.
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PLEASE HELP I GIVE BRAINLIEST
Answers
Answer:
y = 11
Step-by-step explanation:
Perimeter = 6 + 5y + y + 2 + 4y + 3
= 10y + 11
10y + 11 = 121
10y = 121 - 11
= 110
y = 110 ÷ 10
y = 11