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
Describe a real-world situation that could be modeled by dividing two rational numbers.
34kurt

Answer:

Dave got the entire office a loaf of bread and it has 11 slices. There where 4 other people that got the bread including dave how many slices would each person get?

Step-by-step explanation:

just divide 11 by 4

7 0
3 years ago
NEED HELP QUICK!!! WILL GIVE LIKE
AVprozaik [17]
Don’t open the link give you a virus
8 0
3 years ago
Please help I will give brainliest!!
blagie [28]
I am pretty sure it’s the first one
8 0
3 years ago
At 10AM the temperature
Alecsey [184]

Answer:-1 °F

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Which is the graph of f(x) = -(x + 3)(x + 1)?
Furkat [3]

Answer:

It's the second option

Step-by-step explanation:

Graph for -(x+3)(x+1)

4 0
3 years ago
Other questions:
  • Given g(x) = 2x + 5, find g(1)
    5·2 answers
  • Percent equivalent of 7/15
    13·2 answers
  • How to solve this with working out please.
    10·2 answers
  • How do you solve this? 4x(a-4)
    7·2 answers
  • Plz someone help me, this is due in 45mins
    14·2 answers
  • What is the ratio of 420m to 1 km
    13·2 answers
  • Khalid and Jesse took different overnight trains
    10·1 answer
  • four student who work at the the flower shop decided to set up a flower stand in a neighboring town. at the end of the day their
    7·1 answer
  • A snowmobile traveled 32 miles in 2 1/3 hours.
    11·1 answer
  • <img src="https://tex.z-dn.net/?f=x%2By%3D-9%5C%5C%20x%2B2y%3D-25%5C%5Cwhat%20is%20value%20of%20x" id="TexFormula1" title="x+y=-
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!