Answers
You may need to input the number only without the "degrees".
=============================================================
Explanation:
First we'll focus on triangle DEH. Ignore the other points and values.
We have the sides of EH = 32 and DH = 49. Let x be the measure of angle DHE, which is one of the pieces of angle DHG. We'll use the cosine rule to find x.
cos(angle) = adjacent/hypotenuse
cos(H) = EH/DH
cos(x) = 32/49
x = arccos(32/49)
x = 49.227195
The value is approximate and rounded to 6 decimal places. Make sure your calculator is in degree mode. Arccos is the same as inverse cosine.
We'll come back to this value later.
---------------------
Now focus on triangle HFG. Ignore the other points.
We have the sides of FG = 38 and GH = 43
Let y be the measure of angle FHG, which is the missing piece to form angle DHG. Based on how x and y are set up, we can say x+y = angle DHG.
To find y, we'll need the sine rule this time
sin(angle) = opposite/hypotenuse
sin(H) = FG/GH
sin(y) = 38/43
y = arcsin(38/43)
y = 62.094527 which is approximate to 6 decimal places
---------------------
The last step is to add the values of x and y we found earlier
angle DHG = (angle DHE) + (angle FHG)
angle DHG = (x) + (y)
angle DHG = (49.227195) + (62.094527)
angle DHG = 111.321722
angle DHG = 111 degrees after rounding to the nearest whole degree.
----------------------
If you wanted to do this all in one step, you could say:
arccos(32/49)+arcsin(38/43) = 111.3217 which rounds to 111 degrees.
Related Questions
A road is inclined at an angle of 6°. After driving 5,440 feet
along this road, find the driver's increase in altitude. Round to
the nearest foot.
The driver's increase in
altitude is ____ ft.
A. 5,410
B. 569
C. 52,043
D. 572
Answers
========================================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(6) = a/5440
5440*sin(6) = a
a = 5440*sin(6)
a = 568.634840176034
a = 569 feet, which shows why choice B is the answer.
This value is approximate. Make sure your calculator is in degree mode. One way to check is to compute sin(30) and you should get 0.5
side note: 569 feet is roughly equal to 0.1078 miles.
The driver's increase in altitude is 569 feet.
Given that,
A road is inclined at an angle of 6°.
After driving 5,440 feet along this road,
We have to determine,
The driver's increase in altitude?
According to the question,
A road is inclined at an angle of 6°.
After driving 5,440 feet along this road,
The inclination is determined by using the sin angle.
Therefore,
The driver's increase in altitude is,
[tex]\rm Sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\\[/tex]
Where Perpendicular = a, angle = 6 degree and hypotenuse = 5,440ft.
Substitute all the values in the formula,
[tex]\rm Sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\\\rm Sin6 = \dfrac{a}{5440}\\\\\rm 0.104= \dfrac{Perpendicular}{5440}\\\\Perpendicular = 5440 \times 0.104\\\\Perpendicular = 569 \ feet[/tex]
Hence, The driver's increase in altitude is 569 feet.
For more details refer to the link given below.
https://brainly.com/question/11280532
$4000 is compounded annually at a rate of 7% for 7 years.
Answers
Answer:
hey i think its $16,819 i'm so sorry if i get it wrong
Step-by-step explanation:
Addison earns a fixed hourly rate working as a sales clerk. If she works on a holiday, she earns a different hourly rate than she earns on a regular day. In one week, she earns $188.50 by working 5 hours on a holiday and 16 hours during regular days. A different week, she earns $254.00 by working 8 hours on a holiday and 20 hours during regular days.
Answers
Answer:
10.50
Step-by-step explanation:
Select the relation that IS a function.
a. {(-6, -5), (3, 2), (10, 8), (3, 3)}
b. {(-2, -1), (5, -1), (16, 3), (-3, -9)}
c. {(5, 10), (-3, 10), (-3, -10), (4, 7)}
d. {(21, 11), (21, 10), (21, 9), (21, 8)}
Answers
Answer:
B is the function.
Step-by-step explanation:
since there is one y value for every x value we know that is a function
Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
b)
b
17 cm
a
b
8 cm
12 cm
5 cm
Answers
Answer:
a=9.4cm
b=12.0cm
Step-by-step explanation:
Can you guys help I'm having trouble.
Answers
Answer:
given radius =6
Area of triangle =1/2*base*height
=1/2*6*6=18
area of quadrant =1/4πr^2
=1/4*22/7*6*6=22/7*9=198/7=28.2
area of shaded region =area of quadrant -area of triangle
=28.2-18=10.2
What is the answer, What is mCD?
Answers
Answer:
In English, we would call these terms the “Greatest Common Denominator” and the “Least Common Multiple”. It looks like in Italian at least, MCM stands for “Minimo Comune Multiplo” (aka Least Common Multiple) and MCD stands for “Maximo Comune Divisor” (aka Greatest Common Denominator).
Step-by-step explanation:
I hope it works
Larry looked at the clock. It was 9:45 p.m. The bus for his class trip leaves at 8:30 am. How many hours and minutes are there until the bus leaves?
Answers
Answer:
There are 10 hours and 45 minutes until the bus leaves.
Answer:
In between the 10pm to 8 am =10 hours
In between the gap of 9:45 to 10 pm =15 min left
In between 8 and 8:30 am =30 min left
So 10hr and 45 min is the answer
Select 3 side lengths that can form a right triangle.
Answers
Answer:
16 inches, 63 inches, and 65 inches
Step-by-step explanation:
Edit: I had to change cause it was wrong
Answer:
16 inches, 63 inches, and 65 inches
Step-by-step explanation:
16 squared = 256
63 squared = 3969
16 squared + 63 squared = 4225
65 squared = 4225
A^2 +B^2 = C^2
If 1 sec = 5 dots how many dots will there be in 20 secs
Answers
3/5b + (-1/2) = 1/4
solve for the variable.
Answers
Answer:
Step-by-step explanation:
(3b)/5-1/2=1/4
(3b)/5=1/4+1/2
(3b)/5=1/4+(1/2)(2/2)
(3b)/5=1/4+2/4
(3b)/5=3/4
3b=15/4
b=5/4
b=1.25
I need help , I really don’t understand it .
Answers
Answer:
slope intercept form is the form of y=mx+b, where the slope is m and the y intercept is b.
what you have to do is to solve the equations for y.
1) 2x+2y = 10
2y = 10 -2x
y = -x +5
2) 12+4y = -4x
4y = -4x-12
y = -x -3
lines are parallel when they have same slope and different y-intercepts. m1=m2 and b1 ≠ b2
lines are perpendicular when the multiplication of their slope gives -1
m1 x m2 = -1
here the slopes are same and y-intercepts are different so lines are parallel.
find the area of the triangle
Answers
Answer:
area = ½bh
= 1/2×11× 15
= 82.5 Square inches
82.5 Square InchesStep-by-step explanation:15x11/2 = 82.5
Mr. Green baked 24 cookies. 5 sixths of the cookies were oatmeal. How many oatmeal cookies did Mr. Green bake?
Answers
Answer:
20
Step-by-step explanation:
there r 24 cookies
5/6 of 24 is 20 because 24/6 is 4 and 4*5 is 20
Answer:
20 oatmeal cookies
Step-by-step explanation:
If it is 6ths then divide 24 by 6 which is 4 and multiply 5 by 4 which is 20
HELP PLS Last year 15 students earned an A in math class. If I had 128 students, what percent of students did NOT earn an A?
Answers
Answer:
88%
Step-by-step explanation:
128-15=113
113/128=.882
88%
Find the perimeter of the figure below. Notice that one side length is not given.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answers
Answer:
58cm
Step-by-step explanation:
15+14+5+8+6=48
missing side = 15-5 =10
48+10=58
Find the output, b, when the input, a, is 6.
b=17a
Answers
A coffee shop sells a coffee refill mug for $6.75. Each refill costs $1.25. Last month Kim spent $31.75 on a mug and refills. Write an equation you can use to find the number of refills Kim bought. How many refills did Kim buy?
Answers
Answer:
equation: x(1.25) + 6.75 = 31.75 refills: 20
Step-by-step explanation:
The mug costs $6.75, and you aren't buying multiple cups, so that number stays the same. The number of refills is "x" since we do not know the amount. Next to "x" we multiply 1.25 for the cost of each refill. So now we have "x(1.25)" then we add $6.75 to the equation, for the mug price. Along with the total at the end. To which we now have "x(1.25) + 6.75 = 31.75"
Now we solve the equation. First, subtract 6.75 from each side
x(1.25) + 6.25 = 31.75
-6.25 -6.25
Now we have "x(1.25) = 25" So we have to divide each side by 1.25
x(1.25/1.25) = 25/1.25
x = 20
Therefore, Kim bought 20 refills. To check our work we can replace x with 20 in the original equation.
20(1.25) + 6.75 = 31.75
25 + 6.75 = 31.75
31.75 = 31.75
I'm not the best at explanations, but I hope this helped! :)
An 18-feet ladder is leaning against the side of a building. The angle between the ladder and the ground is 30°.
How high up on the building, from the ground, is the top of the ladder?
Answers
9514 1404 393
Answer:
9 feet
Step-by-step explanation:
The sine relation applies.
Sin = Opposite/Hypotenuse
sin(30°) = height/(18 ft)
height = (18 ft)sin(30°) = (18 ft)(1/2)
height = 9 ft
The ladder extends 9 feet up the side of the building.
11/21
as a decimal rounded to the nearest tenth is.....!?
Answers
Answer:
0.5
Step-by-step explanation:
11 / 21 = 0.5238
0.5238
* If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Therefore it's 0.5238 = 0.5
0.5 is the decimal number nearest to tenth of 11/21.
What is Number system?A number system is defined as a system of writing to express numbers.
Given,
11/21
Eleven divided by twenty one.
0.5238
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
0.5 is the decimal number nearest to tenth.
Hence, 0.5 is the decimal number nearest to tenth of 11/21.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ5
What is the range of the function y=-2/3x-10
given a domain of{-9,-3,0,3,9}
Answers
98
kqprhwierui4roqwhrdkej1wddkbrdh
I NEED THE ANSWERS ASAP PLEASE HELP!!!!!
Answers
Answer:
x = 10
y = [tex]10\sqrt{2}[/tex]
Step-by-step explanation:
Let me know if you want an explanation.
It takes 9 hours for 8 men to paint a room,
How many men would be needed to paint the room in 4 hours?
Answers
Answer:
6 people
Step-by-step explanation:
Please help ;-;
2(3x -8y) - 6 =
Answers
Answer:
6x - 16 y -6
Step-by-step explanation:
okay so first you have to distribute the 2 to the number inside the parenthesis
2(3x-8y) -6
you do 2 x 3x, which is 6x
then 2 x -8y, which is -16y
Now the new equation is 6x - 16 y -6
There you go!!
HELP PLEASE!!!!!!!!!!!!!!!!!!!
Answers
Answer:
h=20
i=75
g=55
Step-by-step explanation:
20 is equal to h
75 is equal to i
g looks like its in the middle of them so you would subtract the two and be left with 55
g=55
im not the best at math so im sorry if its wrong.
Answer:
H= 20
I= 75
G= 20
Step-by-step explanation:
Solve the system of equations by graphing.
y = 2x + 5
y = -1/2x
Where do the two lines cross?
Answers
GIVING BRAINLIEST!
What is the slope of the positive graph?
Answers
Answer:
A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y decreases also. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises.
Step-by-step explanation:
245,600,000,000 In scientific notation
Answers
Answer: 2.456 x 10^11
Step-by-step explanation:
You move the decimal to the left until there’s no more zeroes
Answer:
there :D
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
2.456 × 10 to the power of 11
Peter has to spend $9000 on expenses each year. If that amount of money is 60% of his salary, then how much money does Peter make working as an administrator per year?
Answers
Answer:
Step-by-step explanation:
9000 is 60% of what number?
9000=0.6*X
9000/0.6=X
X=$15000
8) Mr. Jones deposited $2,000 into an account. He made no
additional deposits or withdrawals. Mr. Jones earned 4.25%
annual simple interest on the money in the account.
What was the balance in dollars and cents in Mr. Jones
account at the end of 4 years?
Answers
Answer:
2340
Step-by-step explanation: