Answer:
The ratio of two sides of one right triangle is the same of the corresponding sides of any its similar triangles. ... Then a/b = A/B, which means that this ratio is a constant. The same for a/c = A/C, and b/c = B/C
Hope it helps
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We have derived the definitions of the three basic trigonometric ratios sin, cos, and tan using similar right triangles.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
Similar right triangles can be used to derive the definitions of trigonometric ratios, which are commonly abbreviated as sin, cos, and tan.
Consider a right triangle ABC, where angle A is the right angle.
Let's draw another right triangle ABD where angle A is also the right angle and angle B is congruent to angle D.
We say that triangles ABC and ABD are similar, which means that their corresponding angles are congruent and their corresponding sides are proportional.
Let's label the sides of triangle ABC as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side b.
The side opposite angle C is side c.
We can label the sides of triangle ABD as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side x.
The side opposite angle D is side y.
Since triangles ABC and ABD are similar, we can write the following proportion:
b / a = x / y
Solving for b, we get:
b = (x / y) * a
Now, we can use the Pythagorean theorem to relate the sides of triangle ABC:
a² = b² + c²
Substituting b with its value, we get:
a² = ((x / y) a)² + c²
Simplifying, we get:
a² = (x² / y²) a² + c²
Multiplying both sides by y², we get:
a² x y² = x² a² + c² y²
Now, we can solve for x/y, which is equal to sin(B) and y/a, which is equal to cos(B):
sin(B) = x / y = sqrt(a^2 - c^2) / a
cos(B) = y / a = c / a
Similarly, we can consider another triangle ABE, where angle A is the right angle and angle B is congruent to angle E.
We say that triangles ABC and ABE are also similar.
Let's label the sides of the triangle ABE as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side x.
The side opposite angle E is side z.
Using the Pythagorean theorem for triangle ABC, we get:
a² = b² + c²
Substituting b with its value from triangle ABE, we get:
a² = ((z / x) a)² + c²
Simplifying, we get:
a² = (z² / x²) x a² + c²
Multiplying both sides by x², we get:
a² x² = z² a² + c² x²
Now, we can solve for z/x, which is equal to tan(B):
tan(B) = z / x = √(a² - c²) / c
Therefore,
We have derived the definitions of the three basic trigonometric ratios sin, cos, and tan using similar right triangles.
Learn more about trigonometric identities here:
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Sam borrows from the bank $12,000 to buy a car paying in simple interest $ 2,844 per year. Sam paid the loan in 3 years, what is the annual interest rate on the loan?
Answer:
3,468
Step-by-step explanation:
i multiplied 2,844 by 3 and got 8,532 i then subtracted that from 12,000 and got 3,468
describe what congruent figures and similar figures have in common
Answer:
Congruent figures have the same measurements in angles (degrees) and sides (units).
Similar figures are figures that have the same general shape and don't necessarily have to have the same size or measurements.
Something they have in common are corresponding angles and corresponding sides.
A cat can eat 1/2 of a bag of food in 3/4 of a month. How much food can the cat eat in 1 month
Answer:
the cat can eat 1 1/4 bag of cat food n 1 month
Step-by-step explanation:
brainliest plzJamie's company prepares a gift bag for each seat at an awards ceremony. The theater has 30 sections, each with 70 seats. Gift bags for 5 sections will have concert tickets. The rest of the gift bags will have coupons. How many gift bags will have coupons?
Answer:
Step-by-step explanation:
30(total num of sections)-5(amount of sections with concert ticket)=25
25x70(seats per section)=1750
1750 will get coupons
(you dont need the bits in brackets tehy are there to just explain so you know whay and why im doind a calculation)
Hence, the bags will get coupons are [tex]1750[/tex].
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Here given that,
Jamie's company prepares a gift bag for each seat at an awards ceremony. The theater has [tex]30[/tex] sections, each with [tex]70[/tex] seats. Gift bags for [tex]5[/tex] sections will have concert tickets. The rest of the gift bags will have coupons.
Total number of sections are [tex]30[/tex]
Amount of sections with concert tickets are [tex]5[/tex]
So,the gift bags will have coupons is
[tex]30-5=25[/tex]
As each sections has [tex]70[/tex] seats so,
[tex]25[/tex] x [tex]70[/tex] [tex]=1750[/tex]
Hence, the bags will get coupons are [tex]1750[/tex].
To know more about the simplification
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need help so bad pleasss
Answer:
y=2/3x-6
Step-by-step explanation:
i hope this helps :)
pls help! will mark brainliest if correct
Answer:
[tex]x = -2, y = 6[/tex]
Step-by-step explanation:
[tex]-x + 4 = -4x-2[/tex]
[tex]x = -2[/tex]
Plug back into either one of the equations to get y = 6
Write the third missing congruent statement that will allow us to prove the triangles congruent by SAS.
Answer:
LOOK AT YOUR ANSWER IN PICTURE
Find all the missing sides and angles (picture attached)
Answer:
[tex]\boxed{x=73.74}[/tex]
[tex]\boxed{y=16.26}[/tex]
[tex]\boxed{z=25}[/tex]
Step-by-step explanation:
Hello there!
Algebra 1
The first thing we should find is the missing angle
Because this is a right triangle we can solve it using the Pythagorean Theorem
The Pythagorean theorem states that the sum of the two legs squared equal the hypotenuse squared
the formula... [tex]a^2+b^2=c^2[/tex] where a and b = legs and c = hypotenuse
we are given two legs so we plug in a and b and solve for c
[tex]7^2+24^2=c^2\\7^2=49\\24^2=576\\576+49=625\\625=c^2\\\sqrt{c^2} =c\\\sqrt{625} =25\\c=25[/tex]
so we can conclude that the missing side length ( or z) equals 25
now to solve for the angles
Trigonometry
We can solve for y using sin
sin = opposite side divided by the hypotenuse
the opposite of y is 7 and the hypotenuse is 25
so we set up an equation [tex]sin(y)=\frac{7}{25}[/tex]
now we solve for y
[tex]\frac{7}{28} =.28\\arcsin(y)=y\\arcsin(.28)=16.26020471[/tex]
then we round to the nearest hundredth
so we can conclude that angle labeled y = 16.26
basic geometry
Remember all of the angles in a triangle add up to equal 180 so we can find x by subtract the known angles from 180
180 - 90 - 16.26 = 73.74 so we can conclude that x = 73.74
There are 4 consecutive even integers that add up to 268. Which integers are they?
Answer:
4n+ 12 = -268, or 4n = -280, or n = -70. This would imply that the four consecutive ODD integers are -70, -68, -66, -64.
Step-by-step explanation:
Hope this helps :)
Solve for the measure of c. Round decimals to the nearest tenth.
A. 3.7
B. 7
C. 8.8
D. 4.7
Simplify The following Expression:
45 + (x - 12)
Answer:
The answer is x + 33
Step-by-step explanation:
1) Remove parentheses.
[tex]45 + x - 12[/tex]
2) Collect like terms.
[tex]x + (45 - 12)[/tex]
3) Simplify.
[tex]x + 33[/tex]
Therefor, the answer is x + 33.
Answer:
x+33 is your answer
Step-by-step explanation:
45 + (x - 12)
45+x-12
x+45-12
x+33
Which fraction is equivalent to
-(7/8)?
Answer:
35/40
I think that’s what you mean? Hope this helped
Step-by-step explanation:
Please help me with this
Answer:
i cant see it...
Step-by-step explanation:
...
A picture is 5 inches wide and 8 inches tall:
A rectangle is shown. The length of the rectangle is labeled 5 inches. The width of the rectangle is labeled 8 inches.
A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged?
Answer:
area = 250 in²
Step-by-step explanation:
5 x 2.5 = 12.5 in
8 x 2.5 = 20 in
area = 20 x 12.5 = 250 in²
Mrs. Jones rented a truck. Easy math problem. Only answer if you know how to do it. Help needed ASAP
Answer:
80%
Step-by-step explanation:
150/100*20=$30
150-30=120
120/150=0.8=80%
What is the value of X?
A. 6
B. 6√3
C. 12
D. 12√3
Answer:
B
Step-by-step explanation:
sin60°=x/12
⇒x= 6√3
Tina realizes that she needs to figure out the answer to the question, "How many groups of 1/12 are in 2?"
Answer:
24
Step-by-step explanation:
To find how many 1/12 are in 2 divide 2 by 1/12
2/(1/12) = 2 x 12 = 24
Please help! 18/20. Will give brainliest! Spam answers will not be tolerated!
Factor. [tex]2x^5-7x^3-4x[/tex]
[tex]{ \sf{ \: factorise \: \: \: { \underline{ \green{2 {x}^{5} - 7 {x}^{3} - 4x}}}}} \\ \\ { \dashrightarrow{ \blue{ \sf{taking \: x \: common}}}}[/tex]
[tex]{ \leadsto{ \sf{ \green{ \:x(2 {x}^{4} - 7 {x}^{2} - 4)}}}} \\ \\ { \dashrightarrow{ \sf{ \blue{let \: {x}^{2} be \: equal \: to \: a}}}} \\ \\ { \leadsto{ \sf{ \green{ \: x( 2{a}^{2} - 7a - 4)}}}}[/tex]
[tex]{ \leadsto{ \sf{ \green{x(2 {a}^{2} - (8a \: - a) - 4}}}} \\ \\ { \leadsto{ \sf{ \green{x(2 {a}^{2} - 8a + a - 4)}}}} \\ \\ { \leadsto{ \sf{ \green{x(2a(a - 4) + 1(a - 4))}}}}[/tex]
[tex]{ \leadsto{ \sf{ \green{x(2a + 1)(a - 4)}}}} \\ \\ { \sf{ \: now \: putting \: the \: value \: of \: a}}[/tex]
[tex]{ \leadsto{ \green{ \sf{x(2 {x}^{2} + 1)( {x}^{2} - 4)}}}} \\ \\ { \leadsto{ \green{ \sf{ x( {x}^{2} + 1)( {x}^{2} - {2}^{2} )}}}} \\ \\ { \leadsto{ \green{ \sf{x( {x}^{2} + 1)(x + 2)(x - 2)}}}}[/tex]
Help plz ASAP nowwwwwwww
Answer:
y = -3/4x + 5/4
Step-by-step explanation:
Points: (7, -4) and ( -1, 2)
Slope:
m=(y2-y1)/(x2-x1)
m=(2+4)/(-1-7)
m=6/(-8)
m= -3/4
Slope-intercept:
y - y1 = m(x - x1)
y + 4 = -3/4(x - 7)
y + 4 = -3/4x + 21/4
y = -3/4x + 5/4
Answer:
y = -3/4x + 5/4
Step-by-step explanation:
Hope this helps
Brian ate 2/3 of a pizza. His friend, Joseph ate 1/4 of what was left. How much pizza did joseph eat?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] = [tex]\frac{8}{12}[/tex]
[tex]\frac{12}{12}[/tex] - [tex]\frac{8}{12}[/tex] = [tex]\frac{4}{12}[/tex]
[tex]\frac{4}{12}[/tex] * [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{48}[/tex] = [tex]\frac{1}{12}[/tex]
Martin needs to ship a box that weighs 12,000 grams. How should be move the decimal point to convert this number
to kilograms?
O 3 places to the left
O 3 places to the right
O 2 places to the left
O 2 places to the right
Multiply. Reduce if possible, if you can simplify, what is the GCF you used ? what is 3/7 x 2/4
Answer:
3/14
Step-by-step explanation:
A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.
Step-by-step explanation:
the formula can be;
X+9x=10
10x=10X=10/10=1
X=1+9(1)=1+9=10 Answer
Parallel lines and tranvsveral
Answer:
angle 6=54*
Step-by-step explanation:
Transversal lines/alternate angles theorem
find the value of given expression
=》
[tex]32 + 32 \div 32[/tex]
Answer:
32+32÷32=32+1=33 is your answer
Reagan grew 30 plants with 6 seed packets. With 7 seed packets, how many total plants can
Reagan have in her backyard? Assume the relationship is directly proportional.
plants
Submit
Answer:
35
Step-by-step explanation:
6 x 5 = 30
We can assume each seed packet has 5 seeds
6 x 7 = 35
I hope someone knows.
Answer:
x = 9
Step-by-step explanation:
This is a 45-45-90 right triangle so the sides are in the ratio x: x: [tex]x\sqrt{2}[/tex]
After tax and tip,the bill totaled $63.00. What was each persons share? Show your work
If a number is increased by 4, its square is increased by 64. Find the number
Answer:
12
Step-by-step explanation:
12 - 4 = 8
The square of 8 is 64
Answer:
6
Step-by-step explanation:
(n + 4)^2 = n^2 + 64
n^2 + 8n + 16 = n^2 + 64
8n = 48
n = 6
It takes Carol 30 minutes to drive to work using two roads. She drives 24 mph on a small road for hour. Then she drives 56 mph on a highway for hour. How far does Carol travel to work?
Complete question :
It takes Carol 30 minutes to drive to work using two roads. She drives 24 mph on a small road 1/2 for hour. Then she drives 56 mph on a highway for 1/4 hour. How far does Carol travel to work?
Answer:
26 miles
Step-by-step explanation:
The distance traveled is given by :
Distance = speed * time
Distance covered on small road :
24 mph * 1/2 hours = 12 miles
Distance covered in highway :
56 mph * 1/4 hours = 14 miles
Total miles traveled = 12 + 14 = 26 miles