Can someone help me pls

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.

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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Answer:

Step-by-step explanation:

cos 43=cos (90-47)=sin 47

Answer:

the long one because of the friction and you can gain speed the second way

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

2x+3=x

=2x=x-3

=2x-x= -3

= x = -3

i hope this helps :)

Answer:

X=3

Step-by-step explanation:

2x-3=x

Answer:

DC where it at chief, not starting nun just my opinion have a good day

Step-by-step explanation:

here queen/king              

yeah I'll do you one better who's Gamora

Answer:314

Step-by-step explanation:

V=pi r squared

V= 3.14x10 squared

10 squared= 100

V=3.14x 100

V= 314

Answer:

Y=3x-1

Step-by-step explanation:

Let x =1 then ,Y=(3×1)-1=2

Let x=2 then, Y=(3×2)-1=5

Let x=3 then Y=(3×3)-1=8

Let x=0 then Y=(3×0)-1=-1

Answer:

Step-by-step explanation:

Answer:

the answer would be 18.28

Step-by-step explanation:

if you times 0.914 x 20

which would make 20 yards

because 0.914 is only 1 yard

Answer:

Step-by-step explanation:

Parallel lines has the same slope.

The equation of a line that passing through point (x₁, y₁) with a slope of m is:

y - y₁ = m(x - x₁)

m = -3

(-1, 5)   ⇒  x₁ = -1,  y₁ = 5

Therefore the equation:

y - 5 = -3(x + 1)

The mean is the average of the numbers divided by the total number of variables, and the further calculation can be defined as follows:

Calculating the Mean of X:

[tex]= \sum X \times p(X)[/tex]

[tex]= 0\times 0.36 + 1 \times 0.48 + 2 \times 0.16\\\\= 0 + 0.48 + 0.32\\\\=0.80\\\\[/tex]

Therefore, the final answer is "0.8".

Learn more:

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Answer:

-1 dollars

Step-by-step explanation:

Answer:

-0.0016

- 1/ 625

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5 ^ - 4

= 1 / -5 ^ 4

= 1/625

hope it helps :)

Answer:

49.65$

Step-by-step explanation:

(20.40 x 2) + 8.85 = 49.65 $

Answer:

[tex]\displaystyle d = 8\sqrt{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (-4, -4)

Point (4, 4)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

256oz

Step-by-step explanation:

D.

hope this helps have a nice day

Answer:

Option D) 256 oz.

Step-by-step explanation:

Passed the test on T4L 2023 :) Hope this helped

Answer:

sept 30

Step-by-step explanation:

Answer:

$2700

Step-by-step explanation:

Answer:

B. They are similar, but not congruent.

Step-by-step explanation:

Answer:

5h = $150

Step-by-step explanation:

Answer:

150 = 5h

Step-by-step explanation:

h = amount of hours

solve to find amount of hours she needs to work to earn $150

Answer:

Slope (m)= 3

Step-by-step explanation:

m= (Y2-Y1)/(X2-X1)

m= (17-8)/(4-1)

m= 9/3

m=3

Answer:

The answer is 116

Step-by-step explanation:

Because this shape is a quadrilateral, so the sum of the angles of a quadrilateral is a total of 360 degrees. So i added 90 + 90 + 64 = 244. And 360 - 244 = 116.

Answer:

116°

Step-by-step explanation:

There are 2 right angles so we add them:

1 right angle = 90°

2 right angle: 90° + 90° = 180°

As we can we have another value which is 64° so we add that as well:

180° + 64° = 244°

Since it is a 4-sided shape all the values will add up to 360°

Subtract 360 and 244

360° - 244° = 116°

x = 116°

Hope this helps

Answer:

t = 9

Step-by-step explanation:

t/3 = 12 - 9

t = 3 * 3

t = 9

Answer:

t=9

Step-by-step explanation:

t/3+9=12

t/3+9-9=12-9

t/3= 3

3xt/3 = 3x3

t=9

Answer: It would be E

Step-by-step explanation:

Answer:

R17700

Step-by-step explanation:

Dumsani earns R42480 per month. He splits his earnings in the ratio 7:5 and then saves the lesser amount. How much does he save?

First step

We are given the ratio 7:5

The sum of the proportion = 7 + 5 = 12

We are told that he saves the lesser amount

The lesser ratio = 5

Therefore, the amount he saves is

= 5/12 × R42480

= 5 × 3540

= R17700

Therefore, he saves R17700

Answer:

SAS because their is 2 lines and 1 lines

Answer:

The correct option is;

C. This advanced training seminar did not reduce response time, t(35) = -1.43, p > 0.05

Step-by-step explanation:

The given parameters are;

The population mean response time, μ = 9 minutes

The number of police officers in the sample, n = 36

The mean response time after the training, [tex]\overline x[/tex] = 8 minutes

The standard deviation of the response time after the training, s = 4.2 minutes

The level of significance, α = 0.05

The null hypothesis; μ ≥ 9

The alternative hypothesis; μ < 9

The test statistic for the t-test is [tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}[/tex], therefore, we get;

[tex]t=\dfrac{8-9 }{\dfrac{4.2}{\sqrt{36}}} \approx -1.42857142857[/tex]

The degrees of freedom, df = n - 1 = 36 - 1 = 35

The critical-t at 0.05 level of significance is critical-t = 1.69, p(t < -1.43) > 0.05

and, we fail to reject the null hypothesis, therefore, the advanced training did not reduce the response time