What is the exact value of tan(67.5°) ?

Answers

Answer 1

Answer:

[tex]\sqrt\frac{2+\sqrt{2}}{2-\sqrt{2}}[/tex]

Step-by-step explanation:

correct on edge2020

Answer 2

The required exact value of tan(67.5°) is -2 + √(2).

What are trig ratios?

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
The exact value of tan(67.5°) can be found using the half-angle identity for the tangent, which states that:

tan(x/2) = (1 - cos(x)) / sin(x)

We can use this identity with x = 135 degrees since 67.5 degrees is half of 135 degrees. So:

tan(67.5°) = tan(135°/2) = (1 - cos(135°)) / sin(135°)

We can then use the following exact values:

cos(135°) = -√(2)/2

sin(135°) = -√(2)/2

Substituting these values, we get:

tan(67.5°) = (1 + √(2)/2) / (-√(2)/2)

Rationalizing the denominator, we get:

tan(67.5°) = -2 + √(2)

Therefore, the exact value of tan(67.5°) is -2 + √(2).

Learn more about trig ratios here:

https://brainly.com/question/14977354

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Related Questions

What is the value of x in the figure shown below

Answers

Answer:

x = 34 degrees

Step-by-step explanation:

if this is a parallelogram then Δ ACB ≅ Δ DCB

which means that ∠A = ∠D

(5x - 2y = 22
8x - 2y = 28

Please!! Urgent

Answers

9514 1404 393

Answer:

  (x, y) = (2, -6)

Step-by-step explanation:

Subtract the first equation from the second.

  (8x -2y) -(5x -2y) = (28) -(22)

  3x = 6

  x = 2

Substitute this into either equation and solve for y.

  8(2) -2y = 28

  8 -y = 14 . . . . . . . . divide by 2

  y = 8 -14 = -6 . . . . add y-14 to both sides

The solution is (x, y) = (2, -6).

_____

I like a graphing calculator for a quick solution to such problems.

20 points and Brainliest to fastest correct answer!!
In ΔNOP, o = 8.8 cm, n = 3 cm and ∠N=70°. Find all possible values of ∠O, to the nearest 10th of a degree.

Answers

Step-by-step explanation:

function or not a function?

Answers

Can you please get a clearer picture?
The answer is Not a function..

Order from least to greatest
1.84, the square root of 5, 2.3,the square root of 3

Answers

Answer:

square root of 3 ,1.84,2.3, square root of 5

What is the solution to this system of equations?

4y + x = 5

x + 4y = 10

Answers

I Hope it help.
It won’t let me post

the equation doesn't have a solution lol

22 Solve. Type the correct numeric answer in the space provided.
3 1/2 divided by 4 3/8

Answers

Answer:

0.8

Step-by-step explanation:

3 1/2 = 3.5.... 4 3/8 = 4.375

so 3.5 Divided by 4.375 is 0.8

Please give me the correct answer ​

Answers

Number 2 hope this help.

Answer: The fourth set of sides

Step-by-step explanation:

For a set of side lengths to form a right triangle, they have to satisfy the Pythagorean theory [tex](a^{2} +b^{2} =c^{2} )[/tex]

First set of sides

a = 7.5    b = 18    c = 21.5

[tex]a^{2} +b^{2} =c^{2}\\7.5^{2} +18^{2} =21.5^{2} \\56.25 + 324 = 462.25\\380.25 \neq 462.25[/tex]

Second set of sides

a = 7.5   b = 19.5    c = 21.5

[tex]a^{2} +b^{2} =c^{2} \\7.5^{2} +19.5^{2} =21.5^{2} \\56.25 + 380.25 = 462.25\\436.5 \neq 462.25[/tex]

Third set of sides

a = 18     b = 19.25    c = 21.5

[tex]a^{2} +b^{2} =c^{2} \\18^{2} +19.5^{2} =21.5^{2} \\324 + 380.25 = 462.25\\704.25 \neq 462.25[/tex]

Fourth set of sides

a = 7.5     b = 18     c = 19.5

[tex]a^{2} +b^{2} =c^{2} \\7.5^{2} +18^{2} =19.5^{2} \\56.25 + 324 = 380.25\\380.25 = 380.25[/tex]

I hope that helped!

Write down the next two terms in these quadratic sequences:
1.
9, 13, 19, 27,
-

Answers

pretty sure it is ...37, 49

the base of a pyramid has n sides
write an expression for the number of faces on the pyramid

Answers

Answer: The expression for number of faces of a pyramid =1+n

Step-by-step explanation:

A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .

Its base describe the number of other faces of it.

For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....

So the total number of faces in a pyramid = base + lateral faces

If a pyramid has n sides therefore it give rise to n lateral faces such that

The total number of faces in a pyramid= 1+n .


I really need help pls pls pls help

Answers

Answer:

the first one

Step-by-step explanation:

because 1 inch=22feet, so 242 feet=11 inch

what is the slope of the line that passes through (-5,0) and (-5,5)

Answers

Answer:

m=undefined

Step-by-step explanation:

the formula for slope (m) is (y2-y1)/(x2-x1)

here are the given points: (-5,0) and (-5,5)

we can label the points:

x1=-5

y1=0

x2=-5

y2=5

now substitute into the equation

m=(5-0)/(-5--5)

m=(5-0)/(-5+5)

m=5/0

m=undefined

the slope is undefined, because you cannot divide by 0

7xy÷Z=zz please help​

Answers

Could you please write the question more clear?

I'm taking a test and it's really important that I pass it because I'm already failing the class. Please help me I have no idea how to do it. The test has a time limit, everything has to be submitted by 12:25 at the latest. Please show the work if you can.
Simplify the expressions
1. (1+2i)(5-5i)
2. (1+2i)-(-2-2i)
3. (1+2i)+(2-i)
4. (6i)(-5i)

Answers

Answer:

1. 15+5i

2. 3+4i

3. 3+i

4. 30

Step-by-step explanation:

Find the value of X.


Answers

Answer:

In My Knowledge

Option G. 10.4cm is the answer

is there more options

if yes please tell me

I think it’s 10.4 cm not sure tho

Which expression is equivalent to the expression 4(6+y)+7?

Answers

I think it’s 4y+31 but check if it’s correct

Karl drove 619.5 miles. For each gallon of gas, the car can travel 41 miles. What is a reasonable estimate of the number of gallons of gas Karl used?Select all that apply.

Answers

Answer:

15

Step-by-step explanation:

Calculation for What is a reasonable estimate of the number of gallons of gas Karl used

Estimated number of gallons used=619.5 miles/41 miles

Estimated number of gallons used=15

Therefore the reasonable estimate of the number of gallons of gas Karl used is 15

I neeed help it’s a word problem

Answers

Answer:

12.50

Step-by-step explanation:

62/5=12.4

60/2=30

5/2=2.5

i need help with this

Answers

Answer:

30 square cm

Step-by-step explanation:

Key skills needed are: Triangle similarity, multiplication, proportions, subtraction

1) We first find that Triangle BCD is similar to triangle ACE. This is because they both have 1 right angle, and both share Angle BCD. Therefore, the other two angles are also the same measure.

2) Based on the statement above, 6/9 = 8/CE (CE just means the length of CE)

3) Solve this by cross multiplying -

[tex] \frac{6}{9} = \frac{8}{ce} [/tex]

This means that 6(CE) = 8(9)

4) Multiply it out: 6(CE) = 72

5) Divide by 6 and get CE = 12 cm.

6) Then use base time height to find the area of both triangles.

7) For triangle BCD: 6(8)/2 = 6(4) = 24 square centimeters

8) For Triangle ACE: 9(12)/2 = 9(6) = 54 square cm

9) To find the area of ABDE, you would subtract the are of triangle ACE by the area of triangle BCD

10) This is 54 - 24 = 30 square cm.

Hope you understood and have a nice day!! :D

A theater has 384 seats. Each row has 16 seats. The area model represents this situation. Area model showing 2 areas. The first is16 high and 20 wide, with a total of 320. The second is 16 high and x wide, with a total of 64. Part A What is the value of x in the area model? Enter your answer in the box. x = 4 I already answer part A what is the answer for part B?? Part B How many rows of seats are inside the theater? Enter your answer in the box. rows

Answers

Answer:

x=4

Rows = 24

There are 24 rows each having 16 seats making a total of 384.

Step-by-step explanation:

Part B

Total number of seats = Total of rows* Number of seats in each row

Let the total number of rows be y. The theater has 384 seats and each row has 16 seats. Putting the values

384= y * 16

y= 384/16= 24

There are 24 rows each having 16 seats making a total of 384.

Part A:

Area= length * width

Area 1= 320= 16 *20

Area 2 = 64

64 = 16 x

x= 64/16= 4

2*10⁴-7³ please help​

Answers

Answer:

19657

Step-by-step explanation:

By PEMDAS, we know we have to calculate the exponents first, then multiply the 2, and then subtract the 7³

2*10⁴ = 20000

20000 - 7³ = 19657

This is the third time I've seen this question. Are you posting this question again and again?

what is a cereal box an example of

Answers

Answer:

book

Step-by-step explanation:

it has a title,subheading,and more

Answer:

a rectangular prism

Step-by-step explanation:

please help!!!!!(i don't know what else to write so)

Answers

Answer:

A

Step-by-step explanation:

sorry if its wrong but i think its right

WILL MARK BRAINLIEST

What is the rate of change of the linear function that has a graph that passes through the points (1, 15) and (–2, 3)?

Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, . , -, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or decimal.

Answers

Answer:

4

Step-by-step explanation:

Rate of change is just slope, based on what I know.

Given 2 points : (x1, y1) and (x2, y2)... The slope would be [tex]\frac{y_{2}-y_{1} }{x_2-x_{1}}[/tex].

So for this problem we need to find the slope:

(1,15) and (-2,3) are the points. To find slope we do [tex]\frac{3-15}{-2-1}[/tex]. This simplifies into [tex]\frac{-12}{-3}[/tex].This then simplifies into 4.

The rate of change is 4 based on my work.

Can someone help me, if u can ty bless you.

Answers

Answer : 2/3 or 0 R 6

Step-by-step explanation:

hope it helps

please help me please will give brainliest ​

Answers

Answer:

The answer is 32 squares

Answer:

C. 32

Step-by-step explanation:

turquoise paint is made by mixing blue, green and yellow paint in the ratio 2.5 : 1.4 : 0.1 . how much of each colour is needed to make 1.5 litres of turquoise paint? write answers in the same order as the ratio (eg, blue, green, then yellow)​

Answers

Answer: Blue color = 937.5 ml

green color =   525 ml

Yellow color= 37.5 ml

Step-by-step explanation:

Let the quantity of all kinds of paint required to make turquoise paint be 2.5 x(blue), 1.4 x( green), 0.1 x.(yellow).

Total turquoise color required =2.5x+1.4x+0.1x

[tex]\Rightarrow (2.5+1.4+01)x=1.5\\\\\Rightarrow\ 4x = 1.5\\\\\Rightarrow x=\dfrac{1.5}{4}\\\\\Rightarrow\ x=0.375[/tex]  = 1.5 liters  [given]

Blue color = 2.5 x 0.375 = 0.9375 liters = 937.5 ml  [1 liter = 1000 ml]

green color = 1.4 x 0.375= 0.525 l  =  525 ml

Yellow color= 0.1 x  0.375= 0.0375 =37.5 ml

Find the measure of x

Answers

Answer:

x=12

Step-by-step explanation:

6x+7°=8x-17...as opposite <s are =

7+17=8x-6x

24=2x

12=x

1. The value of 20 x 5º =............
2. If a =3 and b=2 then the value of (a + b ) is
3. Angles in a semicircle is
OR
The sum of either pair of opposite angles of a cyclic quadrilateral is
4. Write the degree of the polynomial v2r? +r".
5. The volume of a sphere of radius 3cm is
6. The perimeter of an equilateral triangle is 8 m , what is its area ?
7. In the given figure , AD is the median , then find < BCA
35°
B В
с
D
OBOR
8. A linear equation in two variables has ............ solutions
9. A circle divides the plane on which it lies in
parts.
10. The sum of either pair of opposite angles of a cyclic quadrilateral is.....
11. The formula for finding TSA of a cuboid is
OR
The formula for finding Volume of a cone is
12. In the given figure, find the value of x.​

Answers

Answer: salt

Step-by-step explanation:

Can a right triangle be formed using these squares?
25, 144, 169

Answers

Answer:

Yes

Step-by-step explanation:

The two smaller squares have a sum of 169 which is the value of the larger square.

a^2 + b^2 = c^2

25 + 144 = 169

It can be done. Notice the figure below shows you how to arrange the squares to give the answer of a^2 + b^2 = c^2

Answer:

Yes, if we take the square roots of 25, 144 and 169 (5, 12, 13)

Not by using those measures as is (sides of a triangle with 25, 144 and 169).

Explanation:

A right triangle is a triangle with an angle of 90 degrees, and the side facing that angle of 90 degrees is called an hypotenuse.

The hypotenuse measurement squared is equal to the squared measurements of the other two sides:

c² = a² + b²

And those squares do verify the equation:

169 = 144 + 25

So, that's a rectangle (right) triangle, with sides measuring 5, 12 and 13.

Hope this helps :)

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