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1 month ago

In right triangle ABC, mC - 90° and AC BC. Which trigonometric ratio is cquivalent to sin b?

Mathematics

1 answer:

Zina [12.3K]1 month ago

8 0

Answer:

All trigonometric ratios are $SinB = \frac{AC}{AB}$ , $SinA= \frac{CB}{AB}$ , $CosA= \frac{AC}{AB}$

and $Cos B = \frac{CB}{AB}$ .

Step-by-step explanation:

Provided that

In a right angle triangle ΔABC, ∠C =90°.

The scenario is illustrated below,

In triangle ΔABC:-

$Hypotenuse = AB\\Base = CB\\Perpendicular = AC$

Thus, $Sin\theta = \frac{perpendicular}{hypotenuse}$

$SinB = \frac{AC}{AB}$

Now, in the case of ∠A, the trigonometric ratio dimensions will vary.

Here, the base for ∠A is AC, the perpendicular side is CB, while the hypotenuse remains consistent across ratios

$SinA= \frac{CB}{AB}$

Again, $Cos\theta= \frac{base}{hypotenuse}$

Then, $CosA= \frac{AC}{AB}$

And $Cos B = \frac{CB}{AB}$ .

Therefore,

All trigonometric ratios equal $SinB = \frac{AC}{AB}$ , $SinA= \frac{CB}{AB}$ , $CosA= \frac{AC}{AB}$

and $Cos B = \frac{CB}{AB}$ .

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I trust this will assist you.

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3 months ago

Read 2 more answers

If rs 500 amounts to Rs 725 at 9% simple interest in sometime ,what will Rs 600amount to at 11% in same time?

AnnZ [12381]

Answer:

$Rs\ 930$

Step-by-step explanation:

The formula for calculating simple interest is

$A=P(1+rt)$

Here,

A refers to the Total Amount of Investment

P denotes the Initial Investment

r indicates the interest rate

t represents the duration in time periods

step 1

Determine the duration t

For this scenario, we have

$t=?\ years\\ P=Rs\ 500\\ A=Rs\ 725\\r=0.09$

Plugging into the formula above and solving for t

$725=500(1+0.09t)$

$t=[(725/500)-1]/0.09$

$t=5\ years$

step 2

What will Rs 600 grow to at 11% over the same duration?

We have

$t=5\ years\\ P=Rs\ 600\\ A=?\\r=0.11$

Insert into the formula

$A=600(1+0.11*5)$

$A=600(1.55)$

$A=Rs\ 930$

6 0

2 months ago

Line RS intersects triangle BCD at two points and is parallel to segment DC. Triangle B C D is cut by line R S. Line R S goes th

Zina [12379]

Answer:

The correct statements are;

1) ΔBCD is similar to ΔBSR

2) BR/RD = BS/SC

3) (BR)(SC) = (RD)(BS)

Step-by-step explanation:

1) Since RS is parallel to DC, we conclude that;

∠BDC = ∠BRS (Angles formed on the same side of the transversal)

Furthermore;

∠BCD = ∠BSR (Angles formed on the same side of the transversal)

∠CBD = ∠CBD (Reflexive property)

Thus;

ΔBCD ~ ΔBSR by the Angle-Angle-Angle (AAA) similarity criterion.

2) Given that ΔBCD ~ ΔBSR, we obtain;

BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1

1 + SC/BS = 1 + RD/BR thus, SC/BS = 1 + BR/RD - 1

SC/BS = RD/BR

By inverting both sides we find;

BR/RD = BS/SC

3) From BR/RD = BS/SC, we apply cross multiplication;

BR/RD = BS/SC leads to;

BR × SC = RD × BS → (BR)(SC) = (RD)(BS).

7 0

3 months ago

Which property does each equation demonstrate? x2 + 2x = 2x + x2 (3z4 + 2z3) – (2z4 + z3) = z4 + z3 (2x2 + 7x) + (2y2 + 6y) = (2

babunello [11817]

Response:

1. Closure

2. Distributive

3. Closure

Detailed explanation:

In this scenario, we are examining the properties that each equation demonstrates.

The first equation shows the closure property.

This indicates that whether we add in one direction or the other, the result remains unchanged. Therefore, we conclude that addition conforms to the closure property in this case.

The third equation also shows the closure property. Regardless of how we approach the addition for this equation, the outcome remains consistent.

The second equation displays the distributive property.

Each element within the parentheses is multiplied by the negative sign before we proceed with further calculations.

5 0

2 months ago