A wooden board is leaning against a wall. The base of the board is 10 feet from the base of the wall. The base of the board forms a 35° angle with the ground.
What is the length of the wooden board?
Round your answer to nearest tenth.
Answers
Answer:
The length of the wooden board is about 12.2 feet.
Step-by-step explanation:
Please refer to the diagram attached below.
The base of the board forms a 35° degree angle with the ground.
And we want to find the length of the wooden board.
Since we are given an angle and its adjacent length and we want to find the hypotenuse, we can use the cosine ratio:
[tex]\displaystyle \cos(\theta^\circ)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is the distance from the wall to the board, which is 10 feet.
And the angle made is 35°.
The hypotenuse is the length of the wooden board. Therefore:
[tex]\displaystyle \cos(35)=\frac{10}{\ell}[/tex]
Solve for the length. Cross-multiply:
[tex]\displaystyle 10=\ell \cos(35)[/tex]
Therefore:
[tex]\displaystyle \ell=\frac{10}{\cos(35)}\approx12.2[/tex]
The length of the wooden board is about 12.2 feet.
Related Questions
jason has 60 toy cars 30% of the cars are blue
how many cars are blue?
Answers
Answer: Eighteen toy cars are blue
Step-by-step explanation:
What is the measure of each angle of an equilateral triangle?
A. O 90°
B. O 45°
C. 60°
D. 30°
Answers
Answer:
C) 60 degrees
Step-by-step explanation:
An equilateral triangle has all equal angles. We know that all the angles of a triangle add up to 180 degrees. Therefore 45+45+45=180 giving you an equilateral triangle angle measure.
Fill in the missing blanks for the steps to solve equations with variables on both sides
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Answer:
#2 is combine like terms.
Step-by-step explanation:
How to solve (5x4)^3?
Provide logical explanations as well.
Answers
2 supplementary angles are in the ratio 6:3
Find the angles
Answers
Answer:
The angels are 60 degrees and 120 degrees
Step-by-step explanation:
The sum of two supplementary angels equal 180 degrees.
So, lets look at the ratio: 6:3
We then add 6 and 3 together which gives us 9.
Then you put it in this equation:
9x = 180
x= 20
- You are adding the two numbers and dividing the sum by 180 because the answer will tell us how much 1 would equal.
- In this case, we multiply 20 by 6 = 120 degrees
- Then we multiply 20 by 3 = 60 degrees.
(We can check our answer by: 120 + 60 = 180 degrees) :)
A student in a chemistry lab has access to two acid solution .The first solution is 20% acid and the second is 45% acid .(the percentage are by volume). How many milliliters of each solution the student mix together to obtain 100 ml of a 30% acid solution?
Answers
Answer:
x = 20% acid = 60 ml
y = 45% acid = 40 ml
Step-by-step explanation:
Let
x = 20% acid
y = 45% acid
x + y = 100 (1)
.20x + .45y = .3 ×100
.20x + .45y = 30 (2)
From (1)
x + y = 100 (1)
x = 100 - y
Substitute x = 100 - y into (2)
.20x + .45y = 30
.20(100 - y) + .45y = 30
20 - .20y + .45y = 30
- .20y + .45y = 30 - 20
.25y = 10
y = 10/.25
y = 40 ml
Substitute y = 40 into (1)
x + y = 100
x + 40 = 100
x = 100 - 40
x = 60 ml
x = 20% acid = 60 ml
y = 45% acid = 40 ml
please help i’ll give brainliest
Answers
Answer:
the answer is b
Step-by-step explanation:
because only some of the energy is saved into the body while the other leaves as waste
Which of the following
situations corresponds to
this graph? (Be careful!
The y-axis shows speed, not distance.)
Answers
Camille is attending a fundraiser. She pays for her admission and buys several raffle tickets.
The function S = 5r + 13 represents the total amount of money she paid, S.
and the number of tickets she bought, r. Which is a correct statement?
Camille paid total of $18 at the fundraiser.
The admission was $5.
Camille bought 13 tickets.
The admission was $13.
Answers
Answer: S=5r+85 i think try it out
Step-by-step explanation:
Answer:
The second statement.
Step-by-step explanation:
The function S = 5r + 13 means that the Total = 5 * Tickets + 13 Admission
So if Camille bought 13 tickets, the + 13 at the end means that no matter what, she had 13 dollars admission.
There is a bag filled with 5 blue, 6 red and 2 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 greens?
Answers
Answer:
the probability of getting 2 greens is 2/13
Step-by-step explanation:
Si un empresario paga diariamente 50 a cada trabajador le faltaria 110 pero si les pagara 45 le sobraria 60 cuantos trabajadores tiene dicho empresario
Answers
Answer:
34 trabajadores.
Step-by-step explanation:
Supongamos que el empresario tiene N trabajadores, y tiene la cantidad de dinero D para pagarles cada día.
Si el empresario decide pagarle 50 a cada trabajador le faltan 110.
Esto se puede reescribir como:
50*N = D + 110
(50 por número de empleados es igual que el dinero que tiene más lo que le falta para pagar)
También sabemos que si pagara 45 a cada empleado, le sobraría 60.
Esto se puede reescribir como:
45*N = D - 60
Entonces tenemos dos ecuaciones:
50*N = D + 110
45*N = D - 60
Para resolver esto, el primer paso es aislar una de las variables en una de las ecuaciones, en este caso aislaré D en la segunda ecuación.
45*N + 60 = D
Ahora podemos reemplazar esto en la primer ecuación y resolver para N
50*N = (45*N + 60) + 110
50*N = 45*N + 170
50*N - 45*N = 170
5*N = 170
N = 170/5 = 34
El empresario tiene 34 trabajadores.
SO for this one I'm thinking C but i'm not sure
Answers
Answer: A
Step-by-step explanation: I would say A, because on the left, you have your domain, and the right is your range and codomain.
-4,1,7,15
Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.
Answers
Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form.
It is used in asset (stock) valuation. It is used in bond trading and mortgage calculations.
4 times 8=
PLEASE!!!! tell me the answer!!!
Answers
Answer:
32
Step-by-step explanation:
4*8=32
8+8+8+8=32
4+4+4+4+4+4+4+4=32
Choose the set that is the possible side lengths of a right triangle.
a)1,1,2 b)3,5,9 c)3,4,7 d)1,1,square root2
Answers
Answer:
D
Step-by-step explanation:
Mathematically, for us to have a right triangle, Pythagoras’ theorem must be obeyed
From the theorem, the square of the hypotenuse (longest side) equals the sum of the squares of the two other sides
Let us take a look at the given set of numbers:
2 square is not same as 1 squared + 1 squared
9 squared is not equal to 3 squares + 5 squared
7 squared is not equal to 4 squared + 3 squared
But;
root 2 squared equals 1 squared plus 1 squared and that is our answer
Solve the following problems using Elimination.
NO LINKS PLS-
8x - 5y =-18
2x + 5y = 58
Answers
9514 1404 393
Answer:
(x, y) = (4, 10)
Step-by-step explanation:
The coefficients of y are opposites, so the y-terms can be eliminated by adding the equations.
(8x -5y) +(2x +5y) = (-18) +(58)
10x = 40 . . . . . . simplify
x = 4 . . . . . . . . . divide by 10
Substituting this into the second equation gives ...
2(4) +5y = 58
5y = 50 . . . . . . . . subtract 8
y = 10 . . . . . . . . . .divide by 5
The solution is (x, y) = (4, 10).
Which of these is a simplified form of the equation 13z + 2 = 8 + 2z + 1z? (4 points)
a
10z = 6
b
10z = 10
c
4z = 6
d
4z = 10
Answers
Answer:
a part
Step-by-step explanation:
Answer is attached....
Hope it helps:)
Triangle ABC is a right triangle. The lengths of the legs are 60 centimeters and 80 centimeters.
What is the length, in centimeters, of the hypotenuse?
Answers
Answer:
69.28 cm
Step-by-step explanation:
i used a calculator but the steps you take to solve this are...
1. Multiply the length of one side by the length of the other.
80x60 = 4,800
2. Square that number to get the hypotenuse
[tex]\sqrt48000[/tex]
3. You've got your answer
(69.28)
Answer:
100 cm
Step-by-step explanation:
<3
HELP PLSSSSSSSSSSSSS
Answers
Answer:
x = 4
Step-by-step explanation:
By intersecting secants theorem:
[tex]10(10 + 2x) = 9(2x + 3 + 9) \\ \\ 100 + 20x = 18x + 108 \\ \\ 20x - 18x = 108 - 100 \\ \\ 2x = 8 \\ \\ x = \frac{8}{2} \\ \\ x = 4[/tex]
Number Machine #2
We've built a machine that follows these instructions:
Add 4
Multiply by 2
Subtract 3
Add 4
Multiply by 2
Subtract 3
If we put 10 into this machine, what will come out?
10
Play Store
US na
Answers
10+4=14
14x2=28
28-3=25
"sports discount" has uniforms for 68$. They are offering a 20% discount on each uniform, and a 7 percent sales tax will be applied to the discount price. What would be the final cost for eight uniforms after the discount and sales tax
Answers
Answer:
58.208 times 8 equals 465.664 rounded down to 465.66
Step-by-step explanation:
Answer:
$465.66
Step-by-step explanation:
First, we are buying 8 uniforms. Therefore, the total price on a normal day would be 8x68 = $544
However, on this day, there is a 20% discount. In other words, we are only paying 80% of the original price as percentages are always out of 100.
The price after the sports discount will be 544x0.8 = $435.2
On top of this, we have to pay a sales tax of 7 percent. The 7 percent is an additional cost to the discounted price of 435.2, hence we add 0.07 (7 percent in decimals) onto 1 (100% in decimals).
This gives us 435.2 x ( 1 + 0.07 ) = 465.664.
Because currency is to 2 decimal points (1 cent), the final answer will be 465.66, or 465 dollars and 66 cents.
HURRRYYY PLEASEEE. A ballasted roof is flat and covered with gravel to hold the roofing material in place. Adam plans to cover the roof in the diagram with gravel.
The area that Adam plans to cover with gravel is
. If the weight of the gravel is 12 pounds per square foot, the total weight of gravel on the roof will be
.
Answers
You can’t answer because there is not enough information. You can comment under here and rewrite it or whatever
MARK ME BRAINLIEST PLEASE
Kelly has two dogs, Pixie and Fifi.
Pixie weighs 8.5 kilograms
Fifi is 720 grams lighter than Pixie.
Work out how much Fifi weighs.
Answers
Answer:
7.78 kilograms
George is 6 feet tall and his shadow measured 8 feet long at noon. At the same time, a nearby flagpole cast a 40-foot shadow. What is the height of the flagpole? *
Answers
Answer:
42 I think LOL
“which of the equations below could be the equation of this parabola?”
Answers
Answer: C) y=1/2x^2
Step-by-step explanation:
By using a graphing calculator, we can conclude that the equation y = 1/2x^2 could be the equation of the parabola shown on the graph. (I used Desmos, please see the screenshot below if you have any doubts! :) )
Answer:
c
Step-by-step explanation:
Rectangle JKLM
is rotated to obtain J′K′L′M′
. Which statement is true
a.J′K′L′M′ will be a quadrilateral but not a rectangle because the measurements of line segments and angles are preserved in a rotation, but parallel lines are not.
b.J′K′L′M′ will be a parallelogram but not a rectangle because parallel lines are preserved in a rotation, but the measurements of line segments and angles are not.
c.J′K′L′M′ will be a rectangle because the measurements of line segments and angles, and the presence of parallel lines are preserved in a rotation.
d. J′K′L′M′ will not be a rectangle because the measurements of line segments and angles, and the presence of parallel lines are not preserved in a rotation
Answers
Answer:
Answer is A - Angles that are congruent are complementary to the same angle.
Step-by-step explanation:
trust the process
Please help ASAP I’ll mark you as brainlister
Answers
The diameter is 2 so the radius is 1. The answer is 12.6 if rounded to 1 decimal place.
ANSWER ASAP WILL GIVE BRAINLIEST
in the diagram below what is the approximate length of the minor arc ab
A 31.4
B 14.3
C 7.9
D 15.7
Answers
multiple choice! please help me
Answers
Answer:
they answer is A I think if I'm wrong sorry
How many solutions does this equation have?
8z − 5 = 8z
Answers
Answer:
Zero
Step-by-step explanation:
Solve the equation by subtracting 8z from both sides:
8z − 5 = 8z
-5 = 0
-5 [tex]\neq[/tex] 0
This is a false statement, because -5 is not equal to zero.
This means that there are no solutions to the equation.
So, the equation has zero solutions
Because both sides of the equation have the same variable ( they both have 8x) this equation does not have any solutions.