Explain the cosine rule and sine rule while also saying how to use it and provide examples (keep it in simple terms)

Answers

Answer 1

Answer:

Sure, I'll explain the cosine rule and sine rule in simple terms:

The cosine rule (also known as the law of cosines) is used to find the length of a side or the measure of an angle in a triangle given the lengths of the other sides and the angle between those sides. It states that c^2 = a^2 + b^2 - 2ab cos(C), where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Here's an example of how to use the cosine

Suppose we have a triangle with sides a=6, b=8, and an angle between them c=45 degrees. We want to find the length of the remaining side of the triangle, side a.

Using the cosine rule:

a^2 = b^2 + c^2 - 2bc * cosA

where A is the angle opposite side a, we can plug in our values and solve for a:

a^2 = 8^2 + 6^2 - 2(8)(6) * cos(45)

a^2 = 64 + 36 - 96 * 0.707

a^2 = 10.56

a = sqrt(10.56)

a = 3.25 (rounded to two decimal places)

Therefore, the length of side a is approximately 3.25 units.

Answer 2

Answer:

Step-by-step explanation:

Related Questions

Domingo and Bethany drove along the same highway, in opposite directions. Domingo left at 1 p.m., traveling westbound at 55 mph. Bethany left at the same time, traveling eastbound at 60 mph. Domingo and Bethany were 575 miles apart when they started driving. At what time did they pass each other?

Answers

Step-by-step explanation:

Let's first figure out how far each of them traveled before they meet. Let TIME be the time in hours since they began traveling.

Domingo traveled a distance of 55 * TIME miles

Bethany traveled a distance of 60 * TIME miles

We know that their total distance is 575 miles. So we can write the equation:

55 * TIME + 60 * TIME = 575

Simplifying this equation, we get:

115 * TIME = 575

Dividing both sides by 115, we get:

TIME = 5

So they meet 5 hours after they began traveling. Since Domingo left at 1 p.m., he will meet Bethany at 6 p.m.

They will pass each other at 6 pm.

Given,

Domingo and Bethany drove along the same highway but in opposite direction.

Let's first figure out how far each of them traveled before they meet.

Let x be the time in hours since they began traveling.

Domingo traveled a distance of 55 * x miles

Bethany traveled a distance of 60 * x miles

We know that their total distance is 575 miles. So we can write the equation as,

55 * x + 60 * x = 575

Further simplifying this equation, we get:

115 * x = 575

x = 5

So they meet 5 hours after they began traveling.

Since Domingo left at 1 p.m., he will meet Bethany at 6 p.m.

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!! NEED ASAP !! Write an equation that gives the proportional relationship of the graph.
A) y = 3x
B) y = 12x
C) y = 4x
D) y = 1/4x

Answers

The answer is C y=4c

12x and I did the work that’s why

∠A and ∠B are supplementary angles. If m∠A = (3x+1)∘ and m∠B = (x-9)∘, then find the measure of ∠B.

Answers

Answer:

X= 45

Step-by-step explanation:

So you do

3x+1+x-9=180

Because supplementary angles are 180°

Then

3x+x = 4x

1 - 9 = -10

4x-10=180

4x-10+(10)=180+(10)

4x=190

x=45

Answer:

Step-by-step explanation:

please hurry i need to get this assignment done before friday to get my grade up

Answers

Answer:

y = 2x - 6

Step-by-step explanation:

Answer:

The answer is y = 2x - 6y :)

please please help i need or else i get bad grades

Answers

Answer:

Step-by-step explanation:

all answers on paper!

HELPP QUICK PLS! (50 points and BRAINLY IF ANSWERED CORRECTLY; both; WITH WORK!!!) Silly answers will be reported!

Answers

Answer:

Area of triangle:

(b*h)/2

(16.8 * 14.6)/2 =

122.64m^2

Area of trapezoid:

(a+b)/2*h

(6.7 + 13.6)/2 * 12 =

121.8m^2

Answer: Area of triangle:(b*h)/2(16.8 * 14.6)/2 = 122.64m^2Area of trapezoid:(a+b)/2*h (6.7 + 13.6)/2 * 12 =121.8m^2

Step-by-step explanation:

Write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Answers

Answer: swap u and v I don't think w will change

Step-by-step explanation:

Well if it’s going 180 degrees, then it’s gonna be in Q1. Therefore the numbers would be in the positive, positive section. So U -8 = U’ +8, V = V’ +6 and W = W’ +6. That goes to show that 180 degrees will have the same coordinates.

i really need help with this if anyone can help

Answers

Answer:

6) no, because a tree that is 2 units east and 8 units north would only be one yard away from a pre-existing tree

7) tree A is the closest to the house

8) tree F is the furthest from the house

9) tree D is further east

10) if you were to go 2 yards east and 10 yards north, you would reach tree F

Step-by-step explanation:

hope this helped!

6.no
7.tree A is closest to the house
8.tree F is the furthest
9.tree d is further East
10.if you were to go 2yards east and 10 yards north,you would reach tree F

Write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Answers

Answer: U'=8,5 V'=7,5 W'=6,10

Step-by-step explanation:

The Answer is U=8,5 V=7,5 W=6,10

Noah’s recipe for sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water. a.Noah prepares large batches of sparkling orange juice for school parties. He usually knows the total number of liters, , that he needs to prepare. Write an equation that shows how Noah can find , the number of liters of soda water, if he knows . b.Sometimes the school purchases a certain number, , of liters of orange juice and Noah needs to figure out how much sparkling orange juice he can make. Write an equation that Noah can use to find if he knows .

Answers

Answer: x = T - 4

T = y + 5

Step-by-step explanation:

a. To find the number of liters of soda water (x) if Noah knows the total number of liters (T) of sparkling orange juice he needs to prepare, the equation can be written as:

x = T - 4

b. To find the number of liters of sparkling orange juice (T) Noah can make if the school purchases a certain number of liters of orange juice (y), the equation can be written as:

T = y + 5

In both equations, x represents the number of liters of soda water, T represents the total number of liters of sparkling orange juice, and y represents the number of liters of orange juice.

Answer t=y+5 in the question above

pls help me with this question

Answers

Answer: Its C

Step-by-step explanation: I took the test on Edge.

The answer:
C. 250.8 m^2

PLEASE HELP!! ???? DONT KNOW THIS

Answers

Answer:

Here's the solution I created on Overleaf:

The answer is 29 I believe!

What’s j+12=25 tape diagram

Answers

well you would take 25 and take 12 away. like this: 25-12=? so 25-12 would be 13. therefore j=13!

What is an Equation?

An equation is a mathematical statement that shows two mathematical expressions equal.

An equation consists a variable that does not have a fixed value to it.

Given,

j+12=25

Here ‘j’ is the variable.

To find ‘j’ we just need to 12 from 25.

So, 25 - 12 = 13

Hence, now we know that ‘j’ is equal to 13.

Proof :

13 + 12 = 25

Learn more about Equations here

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Shelby deposited $1,000 in a savings account with simple interest. Two years later, she had earned $80 in interest. What was the interest rate?

pls explain in simple terms

Answers

Her interest was 12.5

You can divide 1000 by 80 and you’ll get the answer

Answer:

4 %

Step-by-step explanation:

simple take 80 times by 100 then divide by 1000 times by 2

Everybody here has one thing in common. what is it?

Answers

Answer: Everyone here most likely sucks at math

Step-by-step explanation:

Brainly gives you answers

We are all lost and confused

please help i need this bad

Answers

Answer:

Step-by-step explanation:

(answer needs to be at least 20 words long)

2) 3 (2.999)
3) 3 (2.958)
4) 2.86 ( 2.815)
5) 2.95 ( 2.949)
6) 3.14 (3.144)
7) 2.84 ( 2.841)

Tom and Katherine live in different towns which are linked by a bike trail. They agree to meet for a bike ride, and both set off from home at the same time. Tom rides north at a speed of 14 mph and Katherine rides south at 10 mph. The bike trail between their homes is 42 miles long. How long will it be before they meet?

Answers

Answer:

We can start by using the formula:

time = distance / speed

Let t be the time (in hours) for Tom and Katherine to meet.

Tom's distance = Tom's speed x time = 14t

Katherine's distance = Katherine's speed x time = 10t

Since they are riding towards each other, the total distance they cover is the sum of their distances:

Tom's distance + Katherine's distance = 42 miles

14t + 10t = 42

Simplifying:

24t = 42

t = 42 / 24

t = 1.75 hours

Therefore, Tom and Katherine will meet after 1.75 hours of riding.

They will meet in 1.75 hours

(ANswer quickly please!) giving brainliest !!!

Last summer, a sports club had 380 members. This summer, due to some renovations, it has 30% more members. How many members are there now?

Answers

Answer:

494

Step-by-step explanation:

380 * 1.3 = 494

494 because 30% of 380 is 114 and 380+114=494

Please hurry i need to bring my grade up before friday

Answers

Answer:

Step-by-step explanation:

1+1 is about 3 so 3

Y=7/4x and I don’t know the y intercept

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