Consider △ABC. Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 13, the length of B C is 12, and the length of A C is 5. What are the angles that make the trigonometric statements true? sin( ) = cos(B) sin(B) = cos( )

Answers

Answer 1

Answer:

22.62°

Step-by-step explanation:

Considering △ABC.  If angle B C A is a right angle, then;

m<BCA = 90 degrees

Given also

AB = 13

BC = 12

AC = 5.

According to SOH, CAH TOA;

Sin <B = AC/AB

Cos <B = BC/AB

Substitute the given values

Sin B = 5/13

B = arcsin(5/13)

B = 22.62

Cos B = 12/13

B = arccos (12/13)

B =22.62

Hence the angles that make sinB = cosB is 22.62°

Answer 2

Answer:

sin(A)=cos(B)

sin(B)=cos(A)

Step-by-step explanation:

I did it, but if you're seeing this, have a good day


Related Questions

Prove that the given quadrilateral is a square. show all the work

Answers

Answer:

A square is defined as a quadrilateral with 4 sides of the same length and 4 right angles. To verify the lengths of the sides, you can use the distance formula. To find the angles, you can use the slopes of the line segments and make sure sides that form an angle have opposite reciprocal slopes.

Step-by-step explanation:

First, find the coordinates of each point. You're provided with the scale and you can just count, but to make it easier, you can label the axes.

A: (0,8)

B: (6,6)

C: (4,0)

D: (-2,2)

The distance formula is used to find the distance between any two points on the coordinate form. Here it is:

d=sqrt((y2-y1)^2 + (x2-x1)^2)

d=distance, and (x1, y1) and (x2, y2) are the points.

Find the length of each side. I'll demonstrate with two sides, AB and BC.

AB: (x1,y1)=(0,8) and (x2,y2)=(6,6)

d=sqrt((6-8)^2 + (6-0)^2)

 =sqrt((-2)^2 + 6^2)

 =sqrt(4+36)

 =sqrt(40)=2sqrt10

BC: (x1,y1)=(6,6) and (x2,y2)=(4,0)

d=sqrt((4-6)^2 + (0-6)^2)

 =sqrt((-2)^2 + (-6)^2)

 =sqrt(4+36)

 =sqrt(40)=2sqrt10

Do the same thing with sides CD and AD, you'll see that they both also have a length of 2sqrt10 inches. (You don't really have to simplify, I just like to.)

To verify if the sides are perpendicular, you need to find the slopes of the sides and make sure that the product of the slopes of each pair of sides that form a vertex is -1. In other words, each pair of sides that form a vertex have to have opposite reciprocal slopes. I'll demonstrate with 2 vertecies, A and B.

To find the slope, you have to use the formula m=(y2-y1)/(x2-x1). m is the slope, and again, (x1, y1) and (x2, y2) are the points you're plugging in.

To find the measure of angle A, you need to find the slopes of sides AD and AB. (These are the sides that meet to form the angle.)

AD: (x1,y1)=(0,8) and (x2,y2)=(-2,2)

m = (2 - 8)/(-2 - 0)

   = -6/-2

   = 3

AB: (x1,y1)=(0,8) and (x2,y2)=(6,6)

m = (6 - 8)/(6 - 0)

   = -2/6

   = -1/3

So AD has a slope of 3 and AB has a slope of -1/3. Now you need to make sure they have a product of -1.

-1/3 * 3 = -1

So yes, it works! As I mentioned before, you can also think of them as opposite reciprocals.

The reciprocal of 3 is 1/3. The opposite of 1/3 is -1/3. So yes, the sides are perpendicular.

Let's do it again with angle B. We have to find the slope of BC now, since we already know the slope of AB.

BC: (x1,y1)=(6,6) and (x2,y2)=(4,0)

m = (0 - 6)/(4-6)

   = -6/-2

   =3

So the slope is exactly the same as the slope of AD. A square is a parallelogram, so it has two pairs of opposite parallel sides. We already verified that 3 and -1/3 are opposite reciprocals, so we now know that angle B has a measure of 90 degrees as well. You can do the same for angles C and D. That way, you'll have proven that all the sides have the same length and all the angles measure 90 degrees-- so the quadrilateral ABCD matches the definition of a square.

Hope this helped!

NEED HELP ASAP
Camille runs every morning before school. On Monday, she ran 2.36 miles. On Tuesday, she ran 4.88 miles. On Wednesday, she ran 3.19 miles. After she ran on Thursday, her total mileage for the week was 12.81 miles. How many miles did she run on Thursday?

Answers

Answer: 2.38

Step-by-step explanation:

Okay so first you add up all the mileage from Monday-Wednesday. After you do that, subtract that number from 12.81 which will give you your answer

Hope this helps :)

How could humans harm biocrusts?

Answers

Answer:

Many human activities can be unintentionally harmful to biological crusts. The biocrusts are no match for the compressional stress caused by footprints of livestock or people or the tracks

Step-by-step explanation:

there are 15 students in a homeroom how many different ways can they be chosen to be elected president vice president or treasurer

Answers


Answer: 455 different ways

(15 x 14 x 13) / (3 x 2 x 1) = 455

I really need help ASAP and I only have 2 left of missing assignments on math and I am really bad at math and I am going to fail help me plzzzzz T^T continue

It's Homework #1: Odds

Answers

6 ) White
5 ) Not sure but my guess would be “B” don’t take my word on this one tho

Answer:

1/5 ; 7/10

Step-by-step explanation:

1) We have 10 letters, G and B are two letters, so the answer is 2/10, that can be simplify in 1/5

2) we have 7 parts black or white. The total parts are 10, so the answer is 7/10

What is not a true statement about the transformation shown below

Answers

Answer:

which transformation. ??

i think you didnt put a screenshot or sum

Step-by-step explanation:

Solve for angle S ? Please help

Answers

Answer:

s= 96

Step-by-step explanation:

s°= 48° +48° (ext. ∠ of triangle)

s°= 96°

s= 96

☆ Exterior angle of a triangle

- The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

Select all valued equal to -4/5
A -4/ -5
B- -4/ -5
C -4/5
D - -4/5
E 4/-5​

Answers

Answer:

i think c and e since it will end with a negative value

You are working on a banner for Friday's pep rally. The length of the banner is 3 times the width. The length is 15 feet. What is the width?​

Answers

Answer:

5 feet

Step-by-step explanation:

15/3 = 5

Your answer is going to be 5ft

pleasssseee helpppppp ill give brainly (if you send a link ill report you)

Answers

Answer:

sorry i am trying but i don't know what to do

Step-by-step explanation:

Answer:

The answer is 10.4 :)

Step-by-step explanation:

125 + 5 x 10.4 will give you your 180 degree angle, therefore 10.4 should be the correct answer! Hope I could help <3

Point F is located at (3, 4) on a coordinate plane. If Point F is reflected across
the x-axis to create Point F', what will the coordinates of F be?

Answers

(-3,4)
Is
The
Correct answer

Find the measure of the indicated angle to the nearest degree

Answers

Answer:

A) 18°

Step-by-step explanation:

To find the measure of the indicated angle, we can use trigonometric ratios.

Looking at the triangle, we can see that we are given the lengths of the two legs of the triangle, but not the hypotenuse. Since we are not given the hypotenuse, the sine and cosine ratios would not work since both of them require the length of the hypotenuse. We can use the tangent ratio, since it only requires the lengths of the two legs. Remember:

[tex]tan(?)=\frac{opposite}{adjacent}[/tex]

From looking at the image, we can see that the length of the side opposite to the angle is 3, and the length of the side adjacent to the angle is 9. Thus, we can use 3 as out opposite and 9 as out adjacent:

[tex]tan(?)=\frac{3}{9}[/tex]

Now we solve for ?. Lets take the inverse tan of both sides to get rid of the tan on the left side:

[tex]?=tan^{-1}(\frac{3}{9})[/tex]

And we get:

? ≈ 18.4349488° ≈ 18°

So the answer would be 18°, or A.

I hope you find my answer to be helpful. Happy studying.

PLSSS HELP (What are the square roots of 25?)

Answers

Answer:

5

Step-by-step explanation:

5*5=25

Answer:

The square root of 25 is 5, -5

Step-by-step explanation:

which expression are equivalent to

A) 1/(-13)^0
B) (-1)^4
C) (-1)^7
D) 1^13
E) 1/13^-1

Answers

Answer:

A.. ....... . . ..........

John has 8 different flags that he wants to hang on the wall. How many different ways can the flags be arranged in a row?

Answers

Answer:

40,320 different ways

Step-by-step explanation:

Here, we want to arrange 8 flags in a row

In the row, there will be 8 places

The first place has 8 flags to be chosen from

The second place has 7 and like that

So mathematically, the number of ways that we can arrange the flags is 8 factorial ways

We have this as:

8! = 40,320 different ways

How would you find: the number, 3/7 of which is equal to t ?

Answers

Answer:

n = (7/3)t

Step-by-step explanation:

Represente the unknown number by n.  Then write the statement symbolically, as:

(3/7)n = t

and then solve the above equation for n by multiplying both sides by (7/3):

n = (7/3)t

Please help.
Is algebra.
PLEASE HELP NO LINKS OR FILES

Answers

it’s B. 7th degree monomial

2(3x-2)+2(2x+7)=30 x=?​

Answers

Answer:

x=2

Step-by-step explanation:

2(3x-2)+2(2x+7)=30

6x-4+4x+14=30

10x+10=30

10x=20

x=2

for this equation i got 2.6 as the answer!

8) Helpppppp please, Thank you.

Answers

Answer:

x = 9

Step-by-step explanation:

What we have here is a bisected angle. What this means is that an angle is being cut in half to create multiple angles. In this case angle E has been bisected. Since that is the case, angles 1 and 2 are equivalent to each other. Now that we know this we can solve for x.

Equation:

x + 8 = 2x - 1

8 = x - 1

9 = x

Daniella earns a 7.5% commission on everything she sells at the electronics store where she works. How much did she earn last week if she sold $3,500 in electronics merchandise

Answers

Answer:$262.50

Step-by-step explanation:3500x.075=262.5

You get a bagel for $1.95 and juice for $1.09. You pay with a 5-dollar bill. How much change will you get back?

Answers

Answer:

$1.96

Step-by-step explanation:

So first what you will do is add 1.09+1.95 then you get 3.04 after that you do 5-3.04 and you get 1.96.  Hope I helped! Have a wonderful day!

Please help me ASAP!!!
A circular pizza has a diameter of 16 inches. Each slice of pizza has a central of angle 45°. What is the area of each slice of pizza?

A. 3.1 in²
B. 6.13 in²
C.25.1 in²
D. 100.5 in²

I know that the area is 8π² I just don't know which answer choice it is.

Answers

Answer:

C.

Step-by-step explanation:

Radius = 16 ÷ 2 = 8

[tex]\frac{45}{360} *8^2*\pi =25.1[/tex] (3sf)

You can first find the total area of the circle which is [tex]64\pi[/tex].

Then, you can find the area of the slice of the pizza, if you take the ratio of the angle it creates with the total angle of a circle (360.)

For example, a semicircle's are would be  [tex]\frac{180}{360} *8*\pi[/tex].

Answer:

C. 25.1 in²

Step-by-step explanation:

Hope this helps

HELP NEEDED ASAP WILL GIVE BRAINLIEST

Answers

40 square inches
I’m pretty sure it’s correct. i’m really just needing more points to help me answer my questions lol!!

In 83.41, which digit is in the tens place?

Answers

Answer: 8

Step-by-step explanation:

80 is in the tens place. second digit left of decimal

Answer:

8

Step-by-step explanation:

80 is in the tens place. second digit left of decimal

Finish solving the equation -13y + 33 = 7.

Answers

Answer:

y = 2

Step-by-step explanation:

-13y + 33 = 7

add -13y to each side of the equation:

33 = 13y + 7

subtract 7 from each side:

13y = 26

divide both sides by 13:

y = 2

-13y + 33 = 7
-13y = 40
y = -3.0769

The measures of the angles of a triangle are shown in the figure below. Solve for x.
42°
(8x+14)
60°

Answers

Answer:

x = 8

Step-by-step explanation:

the sum of all three interior angles in any triangle = 180°

42° + 8x + 14° + 60° = 180°

8x = 180° - 42° - 14° - 60° = 64°

x = 8

Find the slope of the line that passes through the following points: `\left(\frac{2}{5},\frac{2}{3}\right)\ \ \left(-\frac{4}{9},\frac{3}{5}\right)` Show the work/explain!

Answers

Answer:

3/50

Step-by-step explanation:

Slope m = y2-y1/x2-x1

From the coordinate

x1 = 2/5, y1 = 2/3, x2 = -4/9 and y2 = 3/5

Substitute;

m = (3/5 - 2/3)/-4/9-2/3

m = (9-10/15)/(-4-6/9)

m = -1/15/-10/9

m = -1/15 * -9/10

m = 9/150

m = 3/50

Hence the slope of the line passing through the points is 3/50

10.What kind of circle would you need and which direction would the arrow go if you graph x < 1.5 on a number line?

closed circle, arrow goes right

open circle, arrow goes right

closed circle, arrow goes left

open circle, arrow goes left

Answers

open circle, arrow goes left

3. A paint store sells 4 pt of paint for $19. Use a model to write a rate for this situation.
What does this rate mean? Show your work.

Answers

Answer:

4p = 19

p = 4.75

Step-by-step explanation:

p = cost for one pint of paint

Find the surface area of the rectangular prism.
9 cm
15 cm
13 cm

Answers

Answer:

SA = 894 cm²

Step-by-step explanation:

SA = (2 x 15 x 9) + (2 x 13 x 9) + (2 x 15 x 13) = 270 + 234 + 390 = 894 cm²

Answer:

894 cm²

Step-by-step explanation:

[tex]A=2(wl+hl+hw)\\=2(13*15+9*15+9*13)\\=894[/tex]

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