If the area of AABC is D, give the expressions that complete the equation for the measure of ZB?
m
m=
n =
Answers
Given:
The figure of triangle ABC.
The area of the triangle ABC is D.
[tex]m\angle B=\sin ^{-1}(\dfrac{m}{n})[/tex]
To find:
The value of m and n in the given expression.
Solution:
Let h be the height of the triangle ABC.
Area of a triangle is:
[tex]Area=\dfrac{1}{2}\times base\times h[/tex]
Where, b is the base and h is the height of the triangle.
[tex]Area=\dfrac{1}{2}\times a\times h[/tex]
The area of the triangle ABC is D.
[tex]D=\dfrac{1}{2}\times a\times h[/tex]
[tex]2D=ah[/tex]
[tex]\dfrac{2D}{a}=h[/tex] ...(i)
In a right angle triangle,
[tex]\sin \theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin B =\dfrac{h}{c}[/tex]
[tex]\sin B =\dfrac{1}{c}\times \dfrac{2D}{a}[/tex] [Using (i)]
[tex]\sin B =\dfrac{2D}{ac}[/tex]
[tex]m\angle B =\sin ^{-1}\dfrac{2D}{ac}[/tex] ...(ii)
We have,
[tex]m\angle B=\sin ^{-1}(\dfrac{m}{n})[/tex] ...(iii)
On comparing (ii) and (iii), we get
[tex]m=2D[/tex]
[tex]n=ac[/tex]
Therefore, the required values are [tex]m=2D, n=ac[/tex].
Related Questions
EN LA CIMA DE UN FARO DE 7 m DE ALTO SE OBSERVA UNA LANCHA CON UN ANGULO DE DEPRESIÓN DE 12 GRADOS. CALCULAR LA DISTANCIA ENTRE LA LANCHA Y EL PIE DEL FARO
Answers
Answer:
33 metros
Step-by-step explanation:
Esto puede simplemente asimilarse a un problema de trigonometria simple. El Vemos un faro con una altura de 7 m, observando una lancha a 12°. Se pide calcular la distancia de la lancha al faro, pero desde su base.
En este caso, necesitamos determinar ese lado. Observando la figura adjunta, podrás notar que solamente debemos calcular el cateto adyacente del triangulo formado entre el faro y la lancha y sus distancias. Para hacer eso, solo usamos la siguiente función trigonométrica:
tgθ = cat op / cat ady (1)
De ahí despejamos el cat ady:
cat ady = cat op / tgθ
Reemplazando tenemos:
cat ady = 7 / tg12
cat ady = 32.93 m o solo 33 m.
Espero te sirva
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance between the boat and the lighthouse is 32.93 meters.
What is Tangent (Tanθ)?
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
Base is the adjacent smaller side of the angle θ.
Como se da que la altura del faro es de 7 m mientras que el ángulo de depresión es de 12°, por tanto, el ángulo entre el barco y la parte superior del faro también es de 12°.
Ahora, la función tangente de la trigonometría se puede escribir como,
[tex]Tan(\theta)=\dfrac{Perpendicular}{Base}\\\\\\Tan(12^o) = \dfrac{7\ m}{\text{Distancia entre el faro y el barco}}\\\\\\{\text{Distancia entre el faro y el barco}} = \dfrac{7\ m}{Tan(12^o)}\\\\\\{\text{Distancia entre el faro y el barco}} =32.93\rm\ m[/tex]
Por tanto, la distancia entre el barco y el faro es de 32.93 metros.
In English,
The question is AT THE TOP OF A 7 m HIGH LIGHTHOUSE, A BOAT IS SEEN WITH AN ANGLE OF DEPRESSION OF 12 DEGREES. CALCULATE THE DISTANCE BETWEEN THE BOAT AND THE FOOT OF THE LIGHTHOUSE.
As it is given that the height of the lighthouse is 7 m while the angle of depression is 12°, therefore, the angle between the boat and the top of the lighthouse is also 12°.
Now, the tangent function of the Trigonometry can be written as,
[tex]Tan(\theta)=\dfrac{Perpendicular}{Base}\\\\\\Tan(12^o) = \dfrac{7\ m}{\text{Distance between the light house and the boat}}\\\\\\{\text{Distance between the light house and the boat}} = \dfrac{7\ m}{Tan(12^o)}\\\\\\{\text{Distance between the light house and the boat}} =32.93\rm\ m[/tex]
Hence, the distance between the boat and the lighthouse is 32.93 meters.
Learn more about Tangent (Tanθ):
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Please help!! Someone answered this already as a joke, I seriously need help on this
Answers
Match the shape with the correct formula for finding the volume :-
SHAPES :-
ConeCylinder Triangular PrismRectangular Prism PyramidFORMULAE :-
[tex] \sf lwh[/tex] [tex] \sf Bh[/tex] [tex] \sf \frac{1}{3} \pi {r}^{2} h[/tex] [tex] \sf \pi {r}^{2} h[/tex] [tex] \sf \frac{1}{3} Bh[/tex] ____________________Solution :-Given Information :- Shapes Formulae to calculate Volume To Do :-Match the shape with the correct formula for finding the volume.
Calculation :-Cone = [tex] \sf \frac{1}{3} \pi {r}^{2} h[/tex] Cylinder = [tex] \sf \pi {r}^{2} h[/tex] Triangular Prism = [tex] \sf Bh[/tex] Rectangular Prism = [tex] \sf lwh[/tex] Pyramid = [tex] \sf \frac{1}{3} Bh[/tex] ____________________Final Answers :- Cone = [tex] \sf \frac{1}{3} \pi {r}^{2} h[/tex] Cylinder = [tex] \sf \pi {r}^{2} h[/tex] Triangular Prism = [tex] \sf Bh[/tex] Rectangular Prism = [tex] \sf lwh[/tex] Pyramid = [tex] \sf \frac{1}{3} Bh[/tex] ____________________Michelle drives her car around a square track each side of the track is 30 feet long. How many times does the car need to go around the track to go a total distance of1,200 feet/
Answers
Answer:
10 times
Step-by-step explanation:
distance covered once is equal to the perimeter of the square
perimeter of the square = 4 x length
4 x 30 = 120 ft
number of times = 1200 / 120 = 1-
Write 5,890,000,000 in scientific notation.
Answers
BRAINLIEST IF UR CORRECT What is the correct answer?
Answers
Step-by-step explanation:
The function should look like this:
g(x) = 10^(x - 1) + 2
Find the circumference
Answers
Answer:
c=pi*D
d=7
pi times 7= 21.98 is the circumference
c=pi*D
d=8
pi times 8=25.12 is the circumference
Step-by-step explanation:
The cost a dog walker for n hours is given by f(n) = 5 + 10n. Which statement is true?
A. For each additional hour of service, the price of the dog walker increases by $15.
B. For each additional hour of service, the price of the dog walker increases by $5.
C. For each additional hour of service, the price of the dog walker increases by $10.
D. For each additional hour of service, the price of the dog walker decreases by $10.
Answers
Answer:
C. For each additional hour of service, the price of the dog walker increases by $10.
Step-by-step explanation:
Hope this helps!
:)
5 balloons in 12 minutes. At this rate, how many balloons can she blow up in 3 hours?
Answers
Answer:
75 ballons in 3 hours
Step-by-step explanation:
We know the ratio min to balloon, 12:5.
A common factor of 60 is 12 and 5. We know that 5 balloons will come out of the 12 interval mark. [tex]5*5:12*5[/tex] So each hour, we get 25 balloons per hour. Multiply 3 on both sides of the equation to get the total amount of balloons. [tex]5*5*3:12*5*3[/tex]
So, 75 balloons is how many she can blow up in 3 hours.
You walk at a rate of 2 blocks per minute, so you walk 12 blocks in
Blank minutes.
Answers
how do u do number 10?
Answers
Answer:
C is the correct option
Help! Will give out brainliest
Answers
Answer:
75
Step-by-step explanation:
don't know how to explain hope this helps
it would be 75
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the cost to rent a paddleboat at the city park includes an initial fee of $7.00, plus $3.50 per hour. Which equation models the relationship between the total cost, Y, and the number of hours, X, that the paddleboat is rented?
A. y =3.5x+7 B. y =7x+3.5
B. y =7x+3.5
C. y =x/7+3.5 D. y =x/3.57
D. y =x/3.5+7
Answers
Answer:
the correct answer is A, y=3.5x + 7
Simplify the expression below.
Answers
‼️‼️‼️‼️can someone pls explain and what’s the answer? pls:)‼️‼️‼️‼️‼️‼️
Answers
Answer:
4. B
(I'm not positive on what the answer to 5 is, so I won't guess bc I don't want u to get it wrong.)
Step-by-step explanation:
I know that the answer for 4 is B and I'll tell u why. B reads y = 1.5x
This means that when u multiply any number in the row marked "x" by 1.5 it should get the number that's right below it (in the "y" row).
This may sound confusing so let's add some context to it. When we chose the number 20 in the "x" row and multiply it by 1.5 the number we should get has to be 30 bc it's right below 20. In this case it IS so it is a true statement. Make sure to check the statement using different numbers from the row marked "x". (I already checked for u, but it's still a good tip to have )
HOWEVER, when we do a statement that does not correspond to the table
it will not give u a number that's below the row "x". If we use statement A, x = 1.5y that would mean that every number in row "y" should be the number on top of it (row "x") when multiplied by 1.5. This is a false statement bc 60 × 1.5 does not equal 40. If we keep trying with this statement, we will see that it's false. THE EQUATION THAT REPRESENTS THE DATA IN THE TABLE IS B.
The units of area and volume are..
Answers
Answer:
Area is measured in square kilometres
Step-by-step explanation:
Volume measures the space inside a 3-dimensional objects
HELPPPP!!!!
PLZZZZ!!
Answers
Answer:
the 2nd option is true
Step-by-step explanation:
slope for W = 1/2
slope for Z = 1/4
y-intercept for W = -1
y-intercept for Z = -2
y-value when w = -4 is 3 for both W and Z
The length of rectangle PQRS is expressed as 2x+7. The width of rectangle PQRS is expressed as 3x−4. Which expression describes the area of rectangle PQRS?
A.6x^2
B.6x^2-29x-28
C.6x^2-15
D.6x^2+13x-28
Answers
Answer:
[tex]area = length \times width \\ = (2x + 7)(3x - 4) \\ = (6 {x}^{2} - 8x + 21x - 28) \\ = (6 {x}^{2} + 13x - 28) \: sq \: units[/tex]
The area of the rectangle PQRS is given by the formula D) 6x²+13x-28.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
The area of a rectangle is given by the formula:
A = l × w, where l is the length and w is the width.
In this case,
The length is 2x + 7 and the width is 3x - 4.
Therefore, the area of the rectangle is:
[tex]A = (2x + 7)(3x - 4)\\A = 6x^2 - 8x + 21x - 28\\A = 6x^2 + 13x - 28[/tex]
Therefore, the expression that describes the area of rectangle PQRS is D) 6x²+13x-28.
Learn more about algebraic Expression here:
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Giving brainlist to whoever answers
Answers
29
7. Find the least number that must be added to 1300 so as to get a perfect square. Also, find the square root of the
perfect square
Answers
Answer:
69 need to be added
Step-by-step explanation:
1300 +69 = 1369
37 ² = 1,369
square root of 1,369 is 37
6(2x-3) - 2(2x+1)
can someone get an answer for that ASAP pls
no links :)
Answers
Answer: 8x−20
Step-by-step explanation:
Distribute:
=(6)(2x)+(6)(−3)+(−2)(2x)+(−2)(1)
=12x+−18+−4x+−2
Combine Like Terms:
=12x+−18+−4x+−2
=(12x+−4x)+(−18+−2)
=8x+−20
Answer:
[tex]6 \times 2x = 12x\\ 6 \times - 3 = - 18 \\ - 2 \times 2x = 4x \\ - 2 \times 1 = - 2 \\ now \: add \: like \: terms \\ 12x - 4x = 8x \\ - 18 - 2 = 20 \\ \frac{ - 8x}{8} = \frac{20}{8} \\ x = 2.5 \: or \: \frac{5}{2} [/tex]
Step-by-step explanation:
brainiest please
HELP MEEEeeeeeEEEEEEEEEEE
Answers
Answer:
it's neptune hun
Step-by-step explanation:
Answer:
Neptune
Step-by-step explanation:
Like Jupiter and Saturn, Neptune radiates more hear than it receives. ... The average temperature on Neptune is a brutally cold -373 degrees F. Triton, Neptune's largest satellite, has the coldest temperature measured in our solar system at -391 degrees F.
Look at this shape:
Which image shows a translation?
Answers
Answer:
The option C
Step-by-step explanation:
In the option A and B the image is been showed in either up-side down or mirror image. Only the option C has the image in a correct way and just moved the shape in a different position
The solution is Option C.
The image which shows a translation is Figure C.
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the figure be represented as F
Now , the figure is translated up , down, or from side to side
The size of the figure does not change on translation
a)
The figure A has been inverted and it is not a transformation of translation
So , the Figure A is false
b)
The Figure B has been reflected by a factor , and reflection changes the coordinates of the figure F
So , Figure F is False
c)
The Figure C is translated by a factor of x to the left and y to downwards
The size of the figure remains the same
So , Figure C is a translation of Figure F
Hence , the figure C is a translation
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For the quadratic y = x^2 -7x +12, when x = -3, what is the y-value?
Answers
Answer:
y = 0
Step-by-step explanation:
subsitute x = -3 into y = x^2 - 7x + 12
y = -3^2 - 7 x -3 + 12
= 9 - 21 + 12
= 0
Answer: 42
Step-by-step explanation:
y= (-3)^2 -7(-3) +12
= (9) -(-21) +12
= 9+21+12
= 42
Find the surface area of this rectangular prism. 4cm,9cm.5cm
Answers
Answer:
18cm
Step-by-step explanation:
Austin runs 4 miles in 30 minutes. At the same rate, how many miles would he run in 48 minutes?
Answers
Answer:
miles/time = miles/time miles/48 min = 4 mi/30 min ---- miles = 48(2/15) miles = 96/15 miles = 6.4 miles.
Step-by-step explanation:
hope it hlp
Please help!! Thanks in advance!! NO links!!
Kallan will spin each spinner one time. What is the probability that the first spinner will land on a number greater than 7 and the second spinner will land on blue?
Answers
Answer:
probability for numbers greater than seven would be: 5/12
probability for landing on blue would be: 2/8
Step-by-step explanation
first, I counted all of the spaces, then I counted only the blue , or only the numbers over 7.
Which of the following is a true biconditional statement?
O
A. I walk one mile to the store if and only if the store is 5280 feet
away.
B. A person practices yoga if and only the person is relaxed.
c. I wear my raincoat if and only if it is raining.
D. An athlete wears a hat if and only if the athlete is on a baseball
team.
Answers
Answer:
C. I wear my raincoat if and only if it's raining
PLEASE HELPP :(
Does the relationship shown in the table represent a direct or inverse variation relationship?
A: Direct, as x increases, y also increases
B: Direct, as x increases, y decreases
C: Inverse, as x increases, y also increases
D: Inverse, as x increases, y decreases
Answers
Step-by-step explanation:
i think
C: Inverse, as x increases, y also increases
Step-by-step explanation:
C: Inverse, as x increases, y also increases
hope it is helpful to you
how much paper is needed to cover a rectangular bulliten board that is 29 in. wide and 37 in. high?
Answers
Answer:
1073 inches squared.
Step-by-step explanation:
To find how much paper is needed to cover the board, you have to find the area. The formula of area for rectangles is length times width or as you said in the question width times height.
To find the answer:
Area = length * width
Area = 29 * 37
Area = 1073 inches squared.
Don't forget to add the units!
Here is the Math problem.
Answers
Answer:
Workup in photo below.
Step-by-step explanation:
Good luck.