Why does sin54°≈0.809≈cos36° in a right triangle?

A
54° and 36° are complementary angles in the same right triangle. sin54° is the ratio of the opposite leg and the hypotenuse and cos36° is the ratio of the adjacent leg and the hypotenuse. In this triangle, the opposite leg of 54° and the adjacent leg of 36° are the same leg in the triangle.

B
54° and 36° are complementary angles in the same right triangle. sin54° is the ratio of the adjacent leg and the hypotenuse and cos36° is the ratio of the opposite leg and the hypotenuse. In this triangle, the adjacent leg of 54° and the opposite leg of 36° are the same leg in the triangle.

C
54° and 36° are supplementary in the same right triangle. sin54° is the ratio of the opposite leg and the hypotenuse and cos36° is the ratio of the adjacent leg and the hypotenuse. In this triangle, the opposite leg of 54° and adjacent leg of 36° are the same leg in the triangle.

D
54° and 36° are supplementary in the same right triangle. sin54° is the ratio of the adjacent leg and the hypotenuse and cos36° is the ratio of the opposite leg and the hypotenuse. In this triangle, the adjacent leg of 54° and opposite leg of 36° are the same leg in the triangle.

Answers

Answer 1

9514 1404 393

Answer:

A

54° and 36° are complementary angles in the same right triangle. sin54° is the ratio of the opposite leg and the hypotenuse and cos36° is the ratio of the adjacent leg and the hypotenuse. In this triangle, the opposite leg of 54° and the adjacent leg of 36° are the same leg in the triangle.

Step-by-step explanation:

The answer explains itself.

The sum of angles in a triangle is 180°. When one of the angles is 90°, the sum of the other two angles is also 90°. That means those two acute angles are complementary (not supplementary).

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse


Related Questions

how do i do this ? what does the y = 1 have to do with the reflection

Answers

because you have to flip the thing

Can someone help me with the questions in the picture?

Answers

Answer:

25) B obtuse scalene

26) A acute isosceles

27) A acute isosceles

28) D obtuse isosceles

29) D right scalene

30) C obtuse isosceles

31) C obtuse scalene

32) C acute scalene

Step-by-step explanation:

A scalene triangle has sides of no equal measures (no side has the same length as another). An isosceles triangle has two sides of the same length. An equilateral triangle has three sides that all have the same lengths.

An acute triangle has all three angles that each measure less than 90°. An obtuse triangle has one angle that measures greater than 90°. A right angle has one angle that measures exactly 90°.

Hope this helps :)

Which expression best represents the model shown below?
Answer choices
x + 1
2x + 2
x - 1
5x + 5

Answers

x-1

-2x+3x-3+2
x-3+2
x-1

3(x + y) + 2x2 + (1 + y)?

Answers

Answer:

7x+4y+1

Don’t low if you wanted it simplified

Answer:

3x + 4y + 5

Step-by-step explanation:

3(x + y) + 2 • 2 + (1 + y)

3x + 3y + 2 • 2 + (1 + y)

3x + 4y + 4 + 1

3x + 4y + 5

The Idol's Eye diamond weighs 79.2 carats.The Blue Hope diamond weighs 33.68 carats less than the Idol's Eye.What is the weight of the Blue Hope diamond?

Answers

Answer:

45.52

Step-by-step explanation:

Graph the function f(x) = x – 4.
Use the line tool and select two points to graph.

Answers

You should plug this into a graphing calculator on your computer! It helps a lot!

Sa se determine termenii de rang 10,15,20 ai progresiei aritmetice :a)-4,-1,2,5,...;b)10,6,2,-2...;c)1/2,1,3/2,2,...;d)-2/3,-2(6),-4 intregi pe langa 2/3

Answers

Answer:

   

Step-by-step explanation:

help please thank you sm

Answers

the correct answer is 5/21

What is the value of the expression 5ab-2c, where a =2, b=3 and c=0?

Answers

Answer:

30

Step-by-step explanation:

5*2*3 - 2*0 = 30 - 0 = 30

If the side opposite the 60 degree angle in a 30-60-90 degree is 12 centimetres, then what length of the side opposite the 30 degree angle?​

Answers

Answer:

4*[tex]\sqrt3[/tex]

Step-by-step explanation:


PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((

Answers

Answer:

Step-by-step explanation:

Take the two equations and equal them together (2.35 + 0.25x = 1.75 + 0.40x) 2. isolate x onto one side by canceling out (2.35 (- 1.75) + 0.25x (.25x) = 1.75 (-1.75) + 0.40x (.25x) ) 3. get what X equal (x=4) 4. plug the new value of x (4) into ONE of the equations (2.35 + 0.25(4) ) 5. get your answer (3.35)

300% of 82 is what number?

Answers

Answer:246

Step-by-step explanation:

The total cost, c, of buying Mickey Mouse Ears, where m is amount of ears bought and 1 magnet, is given by the formula c = 22m + 8. Which equation is equivalent to this formula when solved for m? *
1 point
m = (c - 8)/22
m = (c+ 8)/22
m = c/22- 8
m = c

Answers

The first one. First you'd subtract 8 from both sides then divide both sides by 22, so it should be the first answer.

que es un experimento determinista

Answers

Answer:

Un experimento determinista es aquel cuyo resultado se puede predecir con certeza de antemano, como combinar hidrógeno y oxígeno o sumar dos números como 2 3. Un experimento aleatorio es aquel cuyo resultado se determina por azar.

Step-by-step explanation:

what is a deterministic experiment

A deterministic experiment is one whose outcome may be predicted with certainty beforehand, such as combining Hydrogen and Oxygen, or adding two numbers such as 2 3. A random experiment is one whose outcome is determined by chance.

During a football game, the parents of the players are selling pretzels and popcorn to make money. They charge $2.50 for a bag of popcorn and $2 for a pretzel. The parents collect $336 in sales. They sell twice as many bags of popcorn as pretzels.

Write a system of equations to represent the situation.

How many pretzels did they sell?

Answers

Answer:

The parents sell 48 pretzels.

Step-by-step explanation:

Let a be the number of bags of popcorn sold, and b the number of pretzels sold.

2.5a + 2b = 336

a = 2b

2.5a + a = 336

3.5a = 336

a = 96

b = 48

f (x) = 2x3 + x2 - 7x + 1 has

Answers

Answer: (x + 2) • (x - 1) • (2x - 3)

Step-by-step explanation:

#1: Solve the linear system below using the elimination method. Type your
answer as an ordered pair in the form (#,#).*
2x + 5y = -16
-3x + 7y = -5

Answers

Answer:

[tex](-3,-2)[/tex]

Step-by-step explanation:

First, you need to get one like term in each equation the same in order to eliminate. To do less damage to the equation, we'll use the x terms.

To get the x terms the same, multiply both equations by the opposite x term:

[tex]-3(2x+5y)=-3(-16)\\\\2(-3x+7y)=2(-5)[/tex]

Simplify by multiplying. Use the distributive property for the left side (remember, two negatives make a positive and a negative multiplied by a positive will always be negative):

[tex]-3(2x)-3(5y)=-3(-16)\\\\2(-3x)+2(7y)=2(-15)\\\\\\-6x-15y=48\\\\-6x+14y=-10[/tex]

Now subtract all like terms. The x terms cancel out:

[tex]-6x-(-6x)=0\\\\-15y-14y=-29y\\\\48-(-10)=58\\\\-29y=58[/tex]

Now solve the new equation for y. Isolate the variable by using inverse operations. The term can be seen as -29×y. In order to isolate the variable, use division (opposite of multiplication). Divide both sides by 29:

[tex]\frac{-29y}{29} =\frac{58}{29} \\\\-1y=2[/tex]

Make the variable positive. Multiply both sides by -1:

[tex]-1(-1y)=-1(2)\\\\y=-2[/tex]

The value of y is -2. Insert this value into either original equation:

[tex]2x+5(-2)=-16[/tex]

Solve for x. Simplify multiplication:

[tex]2x-10=-16[/tex]

Use inverse operations to get like terms on the same side of the equation. Add 10 to both sides (addition is the opposite of subtraction) to cancel out the -10 on the left:

[tex]2x-10+10=-16+10\\\\2x=-6[/tex]

Isolate the variable using inverse operations. The x term can be seen as 2×x. Division is the opposite of multiplication, so divide both sides by 2:

[tex]\frac{2x}{2}=\frac{-6}{2} \\\\x=-3[/tex]

The value of x is -3. Therefore, the solution to the system is:

[tex](-3_{x},-2_{y})[/tex]

:Done

Please help me out! its urgent!

Answers

Answer:

x = 7.5 cm

Step-by-step explanation:

ΔBCA ~ ΔECD ⇒ the corresponding sides are proportional.

[tex]\frac{AC}{DC}[/tex] = [tex]\frac{AB}{DE}[/tex]

AC = 4 + 6 = 10 cm

[tex]\frac{10}{6}[/tex] = [tex]\frac{x+5}{x}[/tex] ⇔ 10x = 6(x + 5) ⇒ x = 7.5 cm

This is the last question on my DBA! Please help!!

What are the key features of the graph's exponential functions? Explain how you find each key
feature and what happens to the graphs if you were to add or subtract a constant term.

Answers

We need the graph to answer!

PLEASE HELP !! 10 POINTS AND BRAINLIEST !! <3

Answers

Answer:

Your answer would be (7, -9)

The answer would be (7, -9)

x2 - 4x + ______________________

Answers

Answer:

4

Step-by-step explanation:

You would complete the square by dividing the b value by 2, and then squaring it. In this case, the b value is -4. You would divide -4 by 2 and get -2. Now, you would square -2, and you would get 4.

How can you tell a triangle is similar with having only one side number?

Answers

Answer:

If the pictures are relevant:

Step-by-step explanation:

Measure the sides, or look for the best fit image

Your job is to sort and stack marblesfor sale. A bag contains 44 marbles, and some green. If there are 11 red marbles, what is the ratio of green to red marbles

Answers

Answer:

3 : 1

Step-by-step explanation:

Given that :

Total Marbles in bag = 44

Color of marbles in bag : red, green

Number of red marbles = 11

The ratio of green to red marbles :

Number of green marbles :

(Total marbles in bag - number of red marbles)

(44 - 11) = 33 green marbles

Hence, ratio of green to red Marbles:

Number of green marbles : number of red marbles

33 : 11

3 : 1

Answer:

The correct answer is 2:1.

Step-by-step explanation:

I did the K12 assignment and is said this was the right answer.  

• You have given an equal sided triangle with side length a. A straight line connects the center of the bottom side to the border of the triangle with an angle of α. Derive an expression for the enclosed area A(α) with respect to the angle (see drawing).

Answers

9514 1404 393

Answer:

  [tex]A(\alpha)=\left\{\begin{array}{ccc}\dfrac{a^2\sqrt{3}\sin{(\alpha)}}{16\sin{(\alpha+\dfrac{\pi}{3})}}&\text{if $\alpha\le\dfrac{\pi}{2}$}\\\\\dfrac{a^2\sqrt{3}}{4}\left(1-\dfrac{\sin{(\alpha)}}{4\sin{(\alpha-\dfrac{\pi}{3})}}\right)&\text{if $\alpha>\dfrac{\pi}{2}$}\end{array}\right.[/tex]

Step-by-step explanation:

If we place the bottom center at the origin and make the sides of the triangle 2 units, then the right side can be described by the equation ...

  y = √3(1 -x)

and the terminal side of the angle α can be described by ...

  y = tan(α)·x

We want the height of the shaded area, which is the y-coordinate of the point of intersection of these two lines.

  y = √3(1 -y/tan(α)) . . . . substituting for x

  y = √3·tan(α)/(√3 +tan(α)) . . . . solved for y

Since we have defined the base of the shaded area to be 1, the shaded area is half this value, or ...

  A(α) = (√3/2)tan(α)/(√3 +tan(α))

Further manipulation can put this in the form ...

  A(α) = (√3/4)sin(α)/sin(α+π/3) . . . . for α ≤ π/2, side length 2

__

For α > π/2, we need to subtract the area A(π-α) from the area of the whole triangle. This gives an area (after some rearranging) of ...

  A(α) = √3(1 -sin(α)/(4·sin(α-π/3))) . . . . for α > π/2, side length 2

__

The problem statement defines the triangle as having a side length of 'a', so the final area formula will be a factor of (a/2)² times the above expressions. That is ...

  [tex]A(\alpha)=\left\{\begin{array}{ccc}\dfrac{a^2\sqrt{3}\sin{(\alpha)}}{16\sin{(\alpha+\dfrac{\pi}{3})}}&\text{if $\alpha\le\dfrac{\pi}{2}$}\\\\\dfrac{a^2\sqrt{3}}{4}\left(1-\dfrac{\sin{(\alpha)}}{4\sin{(\alpha-\dfrac{\pi}{3})}}\right)&\text{if $\alpha>\dfrac{\pi}{2}$}\end{array}\right.[/tex]

_____

The graph (second attachment) shows the area as a function of α (in degrees) for a unit triangle. There are inflection points in the curve at 30°, 90°, and 150°

18/24 greater than or less than 55%

Answers

18/24= 75%
75% is greater than 55%

Answer:

I think 55°% is less

I need help with #22 & 23 ASAP!!!!please explain so I can understand

Answers

Answer:

22.) y = -1/7x + 8/7 23.) y = 2x -3 (x is the slope.)

Step-by-step explanation

22.) Divided each side by 7. Subtract 1/7x from each side to get the eqaution.

23.) Divided each side by 3. Add y to each side. then subtract 9 from each side to get the equation.

A garden bed has 4 sections of vegetables. The garden 8 1/2 yards long.
If each section is equal in the length, what is the length of each section?​

Answers

i think its 12 1/2 because 4 + 8 1/2 = 12 1/2

Answer: 12 1/2

Step-by-step explanation: It is 12 1/2 because you have to multiply 4 times 8 1/2 and you'll get 12 1/2

Thats how you do It and make sure to subscirbe to GamerPlayzSupreme2 BYE!!

What do you call the pairs of roots of quadratic
equation with complex solutions?
Math

Answers

Imaginary numbers
Imaginary numbers contain complex solutions (a +- bi)

What is this in simplest form

Answers

Simplify the expression.

Exact Form:

10/9

Decimal Form:

1.¯1

Mixed Number Form:

1/1/9

Answer:

It would be 1⅑

Step-by-step explanation:

First we turn the fractions into improper fractions.

4 7/9 would now be 43/9

3 2/3 would not be 11/3

Now, we have to make them have the same “bottom number”

3x11=33, 3x3=9

Now our equation is..

43/9 - 33/9 = 10/9

When we turn it into a simplified fraction, it would be 1⅑  

2.4 divided by 16.8 please hurry!!

Answers

0.14285714285

Calculator ;)

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