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
USPshnik [31]
1 year ago
12

Problem 8) In the diagram, RQ ⊥ PQ, m∠QPS = 32°, m∠RPS = 24°, and PQ = 14.Find RS to the nearest tenth of a unit. Image is provi

ded down below. :)

Mathematics
1 answer:
Sav [38]1 year ago
3 0

Since S is a point on the segment QR, then:

QS+SR=QR

Use the diagram and trigonometric relationships to find the value of QS and QR. Then, use the above equation to solve for SR.

In the right triangle PQS, the side QS is opposite to the angle of 32º, and the side PQ is adjacent to the angle of 32º. Then, use the tangent trigonometric function to relate PQ to QS:

\tan\left(32º\right)=\frac{QS}{PQ}

Isolate QS and replace PQ=14:

\begin{gathered} \Rightarrow QS=PQ\cdot\tan\mleft(32º\mright) \\ \operatorname{\Rightarrow}QS=14\tan\mleft(32º\mright) \end{gathered}

On the other hand, notice that the side QR in the right triangle PQR is opposite to the angle QPR, which has a measure of 32º+24º=56º.

Then, by a similar reasoning, we can use again the tangent function to find QR:

\begin{gathered} \tan\mleft(56º\mright)=\frac{QR}{PQ} \\ \Rightarrow QR=PQ\cdot\tan\mleft(56º\mright) \\ \Rightarrow QR=14\cdot\tan\mleft(56º\mright) \end{gathered}

We have found expressions for QS and QR in terms of trigonometric relationships. Then, we can find an expression for SR:

\begin{gathered} QS+SR=QR \\ \Rightarrow SR=QR-QS \end{gathered}

Replace the expressions for QR and QS:

SR=14\tan\mleft(56º\mright)-14\tan\mleft(32º\mright)

Use a calculator to find decimal expressions for tan(56º) and tan(32º). Then, find SR:

\begin{gathered} SR=14\times1.482560969...-14\times0.6248693519... \\ \Rightarrow SR=12.00768263... \end{gathered}

Therefore, to the nearest tenth, the length of the side SR (or RS, which is the same) is 12.0.

You might be interested in
A shipment of 40 fancy calculators contains 3 defective units. What is the probability if a college bookstore buys 20 calculator
JulsSmile [24]

Answer:

38.46%

Step-by-step explanation:

There are no names or marking that can make the calculator look different, so the order is not important. Then we should use a combination to solve this problem.

There are 40 calculators in one shipment, 37 of them good items and 3 of them are defect items. We need to choose 19 good calculators and 1 defect calculator. The number of ways to do that will be:

\frac{37}{19}* \frac{3}{1}= 37!\frac{37!}{19!(37-19!)} * \frac{3!}{1!(3-1)!}= 53017895700

The number of possible ways to choose 20 calculators out of 40 calculators will be:

\frac{40}{20}= \frac{40!}{20!(40-20!)}=137846528820

The chance will be: 53017895700/ 137846528820 = 0.3846= 38.46%

4 0
3 years ago
Patrick raced round a 440 metre circular track and stopped suddenly after 900 metres . How far was she from the starting point a
castortr0y [4]

Answer:

20 meters

Step-by-step explanation:

The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.

So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.

The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be 900-880=20 meters from the starting point.

8 0
3 years ago
I can't get the answer lol
Gelneren [198K]

Answer:

-7/4

Step-by-step explanation:

Recall that slope, m, is defined as the ratio rise to run:  rise/run.

Note that if we start at x = -2 (an arbitrary choice), and move 6 units to the right, we end up at x = 4.  This is the 'run.'  Simultaneously, y starts at 1 and decreases to - 6, a change of -7.  

Thus, the slope of the line through these two points is m = rise/run = -7/4

6 0
2 years ago
Read 2 more answers
FASTTT HURRYYYY PLEASEEEEEE<br> The pair of figures is similar. Find the missing side.
Vladimir [108]
The answer is x=12 :)
6 0
2 years ago
Can you tell me the answer and explanation of this problem
Lyrx [107]

Answer:

Step-by-step explanation:

The Beg balance means what she was having initially =$154.90

The pay check and deposit are credits on her account so they were added.

The wig, shoes and makeup she bought were debits, so they were subtracted

Closing balance is the amount left after the debits have been subtracted from the credits

3 0
3 years ago
Other questions:
  • Charlie mixes 15 liters of 17% acid solution with a 29% acid solution, which results in 23% acid solution.
    12·1 answer
  • The product of t and s less than 3
    11·1 answer
  • Which function and domain could represent the given graph?
    12·2 answers
  • Half if a dozen eggs is 6 eggs.How is 1/2 expressed as a decimal?
    13·1 answer
  • The iron cross is a skiing trick in which the tips of the skis are crossed while the skier is airborne. Find the value of x in t
    15·2 answers
  • 6 cookies cost 36 dollars, what is the price of 1 cookie
    9·2 answers
  • Solve the system of linear equations
    14·1 answer
  • Helphelphelphelphelphelphelphelphelphelphelphelphelphelphelphelpvv
    9·2 answers
  • PLS I BEG I NEED THIS NOW SRY FOR CAPS CANT HELP IT IN RUSH!!!
    15·1 answer
  • Brain if correct help pls
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!