1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gogolik [260]
2 years ago
10

Help with this question.

Mathematics
1 answer:
pychu [463]2 years ago
8 0

Answer:

angleS=83^o

angleR=23^o

Step-by-step explanation:

<h3><u>The Law of Sines</u></h3>

The Law of Sines states that for a given triangle (in a plane), the ratio formed by the Sine of any one of the three interior angles and the side across from it is equal to a common number.

If a triangle is drawn in standard form, with the three vertices identified as A, B, and C, and the interior angles at each vertex simply identified as angleA, angleB, angleC, the sides across from those angles are identified as a, b, and c, respectively.  Given such a labeling for a triangle, the Law of Sines gives the following equation:

\frac{sin(angleA)}{a} =\frac{sin(angleB)}{b} =\frac{sin(angleC)}{c}

From the picture you presented, with triangle RST, side r is on the right and unlabeled, side s is shown in red, and side T is shown in green.  The interior angles for R and S are unlabeled, and angle T is defined as 74 degrees.  The Law of Sines would give the following relationship for your triangle:

\frac{sin(angleR)}{r} =\frac{sin(angleS)}{s} =\frac{sin(angleT)}{t}

Substituting known values...

\frac{sin(angleR)}{r} =\frac{sin(angleS)}{12.7ft} =\frac{sin(74^{o} )}{12.3ft}

It should be noted that without information about the length of side r, angle R cannot be found directly with the Law of Sines because that portion of the equation holds two unknowns.  However, if the other two angles of the triangle are known, angle R can be solved for by using the Triangle Sum Theorem.

<h3><u>Finding Angle S</u></h3>

Focusing in on the ratio with known values on the far right, and the ratio containing angleS first:

\frac{sin(angleS)}{12.7ft} =\frac{sin(74^{o} )}{12.3ft}

... multiplying both sides of the equation by 12.7 ft...

sin(angleS) =\frac{sin(74^{o} ) * 12.7ft}{12.3ft}

Note that the right side of the equation has units of feet in both the numerator and denominator (with no addition or subtraction), so the units will cancel.  Simplifying the right side of the equation by evaluating the expression in a calculator (make sure you're in "degree" mode), will yield a unit-less number:

sin(angleS) = .9925222389...

Undoing the sine function, and solving for the measure of angle S will require taking the "arcsin" of both sides of the equation...

arcsin(sin(angleS))=arcsin(0.9925222389...)\\angleS=arcsin(0.9925222389...)\\angleS=82.98876661...^o\\angleS=83^o<u />

<u />

<h3><u>Finding Angle R</u></h3>

Knowing both angleS and angleT, we can apply the Triangle Sum Theorem to solve for angle R.

Triangle Sum Theorem:  The sum of all 3 interior angles in a triangle (in a plane) is 180 degrees.

angleR+angleS+angleT=180^o\\angleR+83^o+74^o=180^o

Using the subtraction property of equality to isolate angleR and combining like terms...

angleR=180^o-83^o-74^o\\angleR=23^o

You might be interested in
Comment on the relationship between f and P(E) when N is very large. Why do you think the relationship is this way?
melamori03 [73]

Step-by-step explanation:

The goal of any smart investor should be to get the best possible deal when purchasing stock. The better the deal, the higher the potential for profit. In this regard, both a company's P/E ratio and stock price can offer great insight into whether the time is right to buy a given stock.

Stock price

Stock price is simply the amount of money it will cost to purchase a share of a company or fund. Stock prices can fluctuate based on a number of factors. If a company releases a glowing earnings report, then investors will likely feel more optimistic about its potential profitability. Demand for the stock will climb, and so will its price. On the other hand, if a company reports negative earnings or is the subject of bad press, its stock price can quickly fall.

P/E ratio

The P/E ratio measures the relationship between a company's stock price and its earnings per share of stock issued. The P/E ratio is calculated by dividing a company's current stock price by its earnings per share (EPS). If you don't know the EPS, you can calculate it by subtracting a company's preferred dividends paid from its net income, and then dividing the result by the number of shares outstanding.

Let's say a company has net income of $1 billion, it pays $200 million in preferred dividends, and it has 400 million shares outstanding. Here's how we'd calculate its EPS:

($1 billion - $200 million) / 400 million shares = $2 per share

Now that we know the EPS, we can figure out the P/E ratio. If the stock currently trades for $30 per share, then the P/E ratio would simply be $30 divided by $2, or 15.

Stock price and P/E ratio

While a company's stock price reflects the value that investors are currently placing on that investment, a stock's P/E ratio indicates how much investors are willing to pay for every dollar of earnings. The market price of a given stock is needed to calculate its P/E ratio, but in many ways, the P/E ratio offers better insight into the stock's growth potential.

Generally speaking, a high P/E ratio indicates that investors expect higher earnings. However, a stock with a high P/E ratio is not necessarily a better investment than one with a lower P/E ratio, as a high P/E ratio can indicate that the stock is being overvalued. If you invest in an overvalued stock, you run the risk of losing money if it doesn't meet investors' high earnings expectations.

On the flip side, when a company's stock has a low P/E ratio, it may indicate that the stock is undervalued. Investors can often buy undervalued stock at a discount and then profit when the price of that stock climbs. That said, sometimes a low P/E ratio reflects a genuine lack of growth potential.

You can compare a company's P/E ratio with that of similar companies in its industry to get a sense of whether the stock you're looking to purchase is overvalued or undervalued.

Ready to start investing? Head over to The Motley Fool's Broker Center to find the best broker for you and get started today.

5 Stocks that Could Set You Up for Life

I just read that Warren Buffett, the world’s best investor, made over 99% of his massive fortune after his 50th birthday!

It just goes to show you…it’s never too late to start securing your financial future.

And The Motley Fool just released a new report that reveals five of our favorite stocks for building wealth after 50.

And get this, we’re sending a FREE copy of this report to Fool.com readers today.

Simply click here to find out how you can claim your free copy of “5 Stocks for Building Wealth After 50.”

See the stocks now

6 0
4 years ago
My new headset was $99.50 but it was on sale with 30% off. what will i have to pay for it?
DIA [1.3K]

。☆✼★ ━━━━━━━━━━━━━━  ☾

Find the multiplier:

1 - (30/100) = 0.7

Multiply the price by this:

99.50 x 0.7 = 69.65.

You would pay $69.65

Have A Nice Day ❤

Stay Brainly! ヅ

- Ally ✧

。☆✼★ ━━━━━━━━━━━━━━  ☾

7 0
3 years ago
Read 2 more answers
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPP
sineoko [7]

Answer:

I'm pretty sure that it is A- The message travels through the spinal cord

Step-by-step explanation:

3 0
4 years ago
Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.
nevsk [136]
The correct answer is 5/3 .
7 0
4 years ago
2. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and 2-2i.
inna [77]

The polynomial equation for the given roots is x³-7x²+20x-24=0.

Given that, the polynomial equation of the smallest degree whose roots are 3, 2+2i and 2-2i.

Now, we need to write the polynomial equation.

<h3>What is a polynomial equation? </h3>

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation. For an equation to be a polynomial equation, the variable in it should have only non-negative integer exponents. i.e., the exponents of variables should be only non-negative and they should neither be negative nor be fractions.

Now, x=3, x=2+2i and x=2-2i

x-3, x-2-2i and x-2+2i

So, the polynomial equation is (x-3)(x-2-2i)(x-2+2i)=0

⇒(x-3)(x(x-2-2i)-2(x-2-2i)+2i(x-2-2i))=0

⇒(x-3)(x²-2x-2xi-2x+4+4i+2xi-4i-4i²)=0

⇒(x-3)(x²-2x-2x+4-4i²)=0

⇒(x-3)(x²-4x+4+4)=0 (∵i²=-1)

⇒(x-3)(x²-4x+8)=0

⇒x(x²-4x+8)-3(x²-4x+8)=0

⇒x³-4x²+8x-3x²+12x-24=0

⇒x³-7x²+20x-24=0

Therefore, the polynomial equation for the given roots is x³-7x²+20x-24=0.

To learn more about the polynomial equation visit:

brainly.com/question/20630027.

#SPJ1

3 0
2 years ago
Other questions:
  • Which phrases can be used to represent the inequality 12-3x≥9? Check all that apply. (multi choice)
    6·1 answer
  • What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594
    7·1 answer
  • RATIO OF NUMBER OF SKIERS WHO BOUGHT SEASON PASSES TO THE NUMBER OF SNOWBOARDERS WHO BOUGHT SEASON PASSES IS 1:2
    6·1 answer
  • Which is a correct first step in solving 5- 2x &lt; 8x - 3?​
    5·2 answers
  • In the diagram, m = 128° and m = 76°. What is m∠ABC? A. 104° B. 116° C. 128° D. 102° E. 96°
    14·1 answer
  • 56<br>+35<br>24<br>+28<br>57<br>+25<br>3016-56<br>61 8-68<br>10+13: 70+to+3<br>-8013<br>-83​
    9·1 answer
  • PLZ HELP ME my teacher be buggin
    11·1 answer
  • I need help finding y
    7·1 answer
  • A
    6·2 answers
  • Estimate by rounding each decimal to the nearest whole number. 5.85+23.24
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!