Determine whether the statements below are true or false.

Analyze the diagram below and complete the instructions that follow.

lora16 [44]

Answer:

$\displaystyle y=2\sqrt{6}$

$\displaystyle x=2\sqrt{2}$

Step-by-step explanation:

<u>Trigonometric Ratios </u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the right triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The image provided shows a right triangle whose hypotenuse is given. We are required to find the value of both legs.

Let's pick the angle of 30°. Its adjacent side is y. We can use the cosine ration, which is defined as follows:

$\displaystyle \cos 30^\circ=\frac{\text{adjacent leg}}{\text{hypotenuse}}$

$\displaystyle \cos 30^\circ=\frac{y}{4\sqrt{2}}$

Solving for y:

$y=4\sqrt{2}\cos 30^\circ$

Since:

$\cos 30^\circ=\frac{\sqrt{3}}{2}$

$\displaystyle y=4\sqrt{2}\frac{\sqrt{3}}{2}$

Simplifying:

$\displaystyle y=2\sqrt{6}$

Now we use the sine ratio:

$\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}$

$\displaystyle \sin 30^\circ=\frac{x}{4\sqrt{2}}$

Solving for x:

$x=4\sqrt{2}\sin 30^\circ$

Since:

$\sin 30^\circ=\frac{1}{2}:$

$\displaystyle x=4\sqrt{2}\frac{1}{2}$

Simplifying:

$\displaystyle x=2\sqrt{2}$

The choices are not clear, but it seems like the correct answer is C.

$\boxed{\displaystyle y=2\sqrt{6}}$

$\boxed{\displaystyle x=2\sqrt{2}}$

6 0

3 years ago

A used motorcycle is on sale for 3,600

balu736 [363]

What are you looking for? Please ensure that you have copied down the complete original question.

If, for example, the usual price of the cycle is $4,100, and we want to know how much one could save by buying the cycle at $3,600, we must subtract $3,600 from $4,100:

$4,100
- 3,600
-----------
$500

3 0

3 years ago

I need to find the measure of each angle. I don't know where or how to start?

kirill115 [55]

Answer:

40°

Step-by-step explanation:

Every triangle adds up to 180°

So to get the angle of the triangle we already have two values of:

$180 - 79 - 52 = 50$

Then since it's at a 90° angle we can subtract 50 to get:

40° as the other part of the right angle.

And applying the 180 rule again:

$180 - 100 - 40 = 40$

7 0

3 years ago

June elloy makes a 22 percent down payment on a home in Rockford, Illinois. What is the purchase price of the home assuming her

Bogdan [553]

22%/100=.22

.22*35,200=11,616 (This is 22% of 35,200)

answer $11,616

6 0

3 years ago

Read 2 more answers

A teacher wants to know whether their course helps students on the SAT. The hypothesized population mean for SAT scores is 500.

Natali5045456 [20]

The z-score is -0.428

<h3>What is a z-score?</h3>

A z-score, also known as a standard score, provides information on how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve.

You must be aware of the mean and population standard deviation to use a z-score.

Z-scores allow results to be compared to a "normal" population.

According to the question,

x=500

μ=533

σ=77

z-score=(x-μ)/σ

On substituting the values,

z-score=(500-533)/77

= -0.428

Learn more about z-scores here:

brainly.com/question/25638875

#SPJ4

8 0

1 year ago