Show that the cosine law simplifies to the Pythagorean theorem when the contained angle between the two known sides is 90°.

Answers

Answer 1

Answer:

See Below.

Step-by-step explanation:

We want to show that the Law of Cosines simplifies to the Pythagorean Theorem when the contained angle between the two known sides is 90°.

The Law of Cosines is given by:

[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]

Where a and b are the two known sides, and C is the angle between them.

If C is 90° then we will have:

[tex]c^2=a^2+b^2-2ab\cos(90 ^\circ)[/tex]

Recall that the cos(90°)=0. Hence:

[tex]c^2=a^2+b^2-2ab(0)[/tex]

Simplify:

[tex]c^2=a^2+b^2[/tex]

So, we acquire the Pythagorean Theorem as desired.


Related Questions

How do you solve problems involving sequence? Discuss the mathematics concepts and principles applied when solving problems involving sequence

Answers

Step-by-step explanation:

Sequence is defined as arrangement f numbers in a specific or defined pattern. Sequence are categorized into

1) Arithmetic

2) Geometric

Arithmetic sequence are characterized by their common difference while Geometric sequence are characterized by their common ratio.

Given a sequance of numbers say;

T1, T2, T3...

The first term "a" of the sequence is T1

Common difference d = T2-T1 =T3-T2

Common ratio = T2/T1 = T3/T2

The formula for calculating nth term of an Arithmetic sequence is expressed as;

Tn = a+(n-1)d

a is the first term

n is the number of terms

d is the common difference

The nth term of a Geometric sequence is expressed as;

Tn = ar^{n-1}

r is the common ratio

Numbers are arranged in a sequence when they follow a predetermined or established pattern. Sequences can be divided into

1) Mathematics

2) Graphitic

Geometric sequences are characterized by their common ratio, whereas arithmetic sequences are distinguished by their common difference.

Suppose a sequence of numbers is given;

T1, T2, T3...

The sequence's initial term "a" is T1.

common distinction d = T2-T1 =T3-T2

T2/T1 Common Ratio T3/T2

The following is the formula for finding the nth term in an arithmetic sequence:

Tn = a+(n-1)d

The first term is a.

The number of terms is n.

d is the typical discrepancy

The nth term of a Geometric sequence is expressed as;

[tex]T_{n} =ar^{n-1}[/tex]

r is the common ratio

To learn more about information Sequence :

brainly.com/question/28015562

what do i say for this
please help :((((

Answers

Answer:

Step-by-step explanation:

Error 1) It should be divided by 5.

x - 5 = 0

x = 5

Error 2) -3   15   0    -1     5

coefficient of x² is 0 and it is not included

Solve this equation




3|6v+2|=-66

Answers

I believe it’s no solution

Derrick is placing a right triangle in the coordinate plane. He knows that the longer leg is 3 times the length of the shorter leg. He places the longer leg on the x-axis.

What coordinates should he assign to the third vertex of the triangle?

Answers

Answer:

Longer leg is placed on X axis.

Let the longer leg be at A(0,0) and B(3 a,0),or (-3 a,0), which is  either base or altitude.

AB= 3 a

As longer leg = 3 × shorter leg

Shorter leg should be placed  either at (0,a) or (0,-a) maintaining triangle as right angled triangle.

Step-by-step explanation:

calculate the value of the expression (-8)·(-1/3)​

Answers

Answer:

8/3

Step-by-step explanation:

If we multiply it the subtraction will cut off and 8 will mulitply to 8/3.

Ratio to 6:3?? Write 2 other ways :))

Answers

Answer:

6/3, 6:3, and 6 to 3

Step-by-step explanation:

All of these answers above are correct!!!

May I have a Brainliest?

As a salesperson, you are paid $150 per week plus $5 per sale that you make. This week
you want your pay to be at least $225. Write and solve an inequality for the number of
sales you need to make

Answers

Answer:

15 Sales

Step-by-step explanation:

225 - 150 = 75

75 / 5 = 15

Solve the equation 2 + 4.7 = -9.3.

Answers

Answer: positive then greater than

Step-by-step explanation:

2 + 4.7 = 6.7
Therefore, the it is a positive number that is greater than -9.3.

Tracy can type 45 words in 3 minutes. At that rate, how many minutes would it take Tracy to type 315 words?​

Answers

Answer:

21 minutes

Step-by-step explanation:

The rate that she types is 15 words in a minute

315/15 =

21 or 21 minutes

Answer:  It will take Tracy 21 minutes to type 315 words

Step-by-step explanation:

Set up a proportional relationship to solve for the  number of minutes.

45 words  = 3 mins

315  words =  x mins.  

[tex]\frac{45}{315} = \frac{3}{x}[/tex]      Cross multiply  

45x = 945    Divide both sides by 45

 x = 21  

O There are 15 students going on a field trip. If 3/5 of them pack their lunches, how many students pack their lunches?

Answers

Answer:

Students

Step-by-step explanation:

Consider these functions:
f(x)=3x - 7
g(t)=1+1
What is the value of f(g(3))?
A.-1

B.0

C.3

D. 5

Answers

Answer:

A(-1)

Step-by-step explanation:

First, we will replace any x in g(x) with 3

g(x)=(3+1)/(3-1)=4/2=2

Thwn replace any x in f(x) with 2

f(x)=3(2)-7=6-7=-1 ⇒A

hope this helps

What is the inverse of the function f(x) = x +3

Answers

Answer:

h(x) = x-3

Step-by-step explanation:

The inverse of a function works such that f(h(x)) = x. Also, f(h(x)) = h(x) + 3. Thus, x = h(x) +3 -> h(x) = x-3

i hope this helps!!! :)

all my points! PLZ help me on this and explain ur answer plzz

Answers

It’s already answered in the other post and sorry if I didn’t answer in this post

Find the perimeter of the figure. Round to the nearest tenth if needed.
a=50 b=83 c=65

Answers

Answer:

263

Step-by-step explanation:

50 + 83 + 65 + 65 = 263

i don’t know witch sides are which but here you go

Describe the end behavior of the polynomial function.

Answers

Rises to the left and rises to the right

microzooplankton is _____ compared to macrozooplankton

a) smaller
b) bigger
c) faster
d) brighter in color

btw yes i put it on math because i feel like more people do math more

Answers

a ) smaller is correct answer

3x-y=6
-4x+2y=-8 solve using substitution method

Answers

Answer:

x=  3y+2

Step-by-step explanation:

The purchase price of an iPad is $625.00. There is a 15% discount and the tax rate is
8%. What is the total cost of the iPad?

Answers

Answer:

$573.75

Step-by-step explanation:

625.00x15%=93.75

625.00-93.75=531.25

531.25x8%=42.50

531.25+42.50=573.75

Answer: I think that the answer is $573.75

please correct me if im wrong.

Step-by-step explanation:

Quadrilateral MNOP is similar to quadrilateral SURT

Answers

Answer:

C is the anser i belive i im wrong im sorry

Step-by-step explanation:

What is the point-slope form of an equation passing through (0, -5) with a 5 points
slope of 2? *

Answers

Answer:

y=2x-5

Step-by-step explanation:

[tex]y-y_{1}=m(x-x_{1})[/tex]

[tex]x_{1}=0, y_{1}=-5\\[/tex], and m=2

[tex]y-(-5)=2(x-0)[/tex], -(-5)-Two negatives make it positive, and you distribute the 2

[tex]y+5=2x[/tex], you now subtract 5 to get y by itself to get your answer of

[tex]y=2x-5[/tex]

*NOTE* (0,-5) is the y-intercept, so you could have used the linear equation of y=mx+b, m=2, and b(y-intercept)=-5

giving you y=2x-5

Please help, I am bad at math and I don't know how to answer this question please help

How is solving equations with fractions similar to solving equations with whole numbers?

(Written Response)
(Sorry if this is easy, if you have already done this on edg, I don't mind if it is the sample response)

Answers

Answer:

You have to make the fraction into a whole number.

Step-by-step explanation:

Hope this helps. :)

Can you guys help me find the slope for the given graph and y-intercept
(pictures included)

Answers

Answer:

I believe the answer is

[tex]y = \frac{2}{3} x + 1[/tex]

slope = 2/3x

y-intercept = 1

Step-by-step explanation:

Hope this helps!

ILL MARK U BRAINLIEST HELP

Answers

Answer:

6x-y

Step-by-step explanation:

Add the two expressions

Answer:

6x + -y

Lets simplify this step by step:

2x + 7y + 4x −8y

2x + 7y + 4x + −8y

Then we combine like terms

=2x + 7y + 4x + −8y

=(2x + 4x) + (7y + −8y)

= 6x + −y

Juan needs to take an Uber to get to the movies. The Uber charges $1.50 for the first mile, and then $1.55 for each mile after that. If the total charge is $10.49, then how far was Juan’s Uber ride to the movie?

Answers

Answer:

5.8 miles were travelled by Juan's Uber ride to the movie.

Step-by-step explanation:

Let x = miles travelled by Juan

Charges for first mile = $1.50

Charges for each mile after first = $1.55

Total charge for Juan = $10.49

We need to find how many miles Juan covered?

The equation will be:

[tex]1.50+1.55(x)=10.49[/tex]

We will solve this equation to find value of x

Solving:

[tex]1.50+1.55(x)=10.49[/tex]

Subtracting 1.50 from both sides

[tex]1.50+1.55(x)-1.50=10.49-1.50\\1.55(x)=8.99\\x=\frac{8.99}{1.55} \\x=5.8[/tex]

So, 5.8 miles were travelled by Juan's Uber ride to the movie.

Each cable car at an amusement park can hold six Riders. There are 51 people in line to ride the cable cars. How many cable cars will the people in line fill? how many more people are needed to fill the next cable car? ​

Answers

Answer:

9 cable cars

Step-by-step explanation:

51 ÷ 6 = 8.5

8.5 rounds up to 9

Answer:

3

Step by step explanation:

54 ÷ 6 = 9

help helppppppppppppp

Answers

Answer:

4/15 = height of lamp/(15+5)

4/15 = height of lamp/20

20/15 = 1 5/15

1 5/15 times taller

lus
If f(x) = 3x + 7, find:
f(3) = [?]

Answers

Answer:

The answer is 16

Step-by-step explanation:

You substitute 3 in for x.

Please help me! Itll mean so much!

Answers

because all angles of a triangle add up to 180 and we already know two of the angle values you would subtract them from 180 to get your answer
180-45-55=80

your answer is 80 degrees
i think it’s 80 degrees

Please help asap!! Due today!

Answers

Answer:

No for the first

Step-by-step explanation:

Sorry i do not know the second one bt the first one is No it is not a right angle

Brett bought 2 shirts. One cost $4 more than 3 times the other. Together, the 2 shirts cost
him $72.

HELP PLEASE.

Answers

Answer:

one costs 17 dollars the other costs 55 dollars

Step-by-step explanation:

we have to make 2 equations using variables

x=shirt 1

y= shirt 2

y+x=72

x=3y+4

then substitute 3y+4 for x in the first equation

y+3y+4=72

subtract 4 and add y and 3y

4y=68

divide by 4

y= 17

use this for y in the second equation

x=3(17)+4

x=51+4

x=55  

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