Can someone help with questin 1 and 2.

Mathematics

1 answer:

aleksandrvk [35]2 years ago

5 0

Answer: are you single

Step-by-step explanation:

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Angle Relationships

leva [86]

Answer:

B. 14 ft

Step-by-step explanation:

I calculated it logically

6 0

2 years ago

Read 2 more answers

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

Sav [38]

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: