Given: △pqr, m∠r = 90°, mp = 18 m∠pqr = 75°, m∠mqr = 60° find: rq

Correct answer is RQ=9

Solution:-

Given that in a ΔPQR, m∠R=90°, MP=18, m∠PQR=75° and m∠MQR=60°.

Since m∠MQR<m∠PQR, M should lie on PR only, Please refer the diagram attached for reference.

From the diagram∠PQM=∠PQR-∠MQR=75°-16°=15°

And in ΔPQR,∠RPQ=180-(remaining 2 angles in triangle)

                                =180-(90+75)=15°

So, in ΔPQM, ∠MPQ=∠PQM hence the opposite sides must be equal that is

    MP=MQ but given MP=18

Hence MQ=18

In ΔMRQ, cos(∠MQR)=

                cos(60°)=

                RQ= 18cos(60°)=18X0.5 =9

Hence RQ=9

RQ = 9

Step-by-step explanation:

In the given triangle,

∠R = 90° , ∠PQR = 75° , ∠MQR = 60° and MP = 18

From the diagram

                       ∠RPQ = ∠ PRQ - ∠PQR = 90° - 75° = 15°·············(1)

In ΔMPQ

               ∠MQP = ∠PQR - ∠MQR = 75° - 60° = 15°·················(2)

from (1) and (2)

                          ∠RPQ = ∠MQP = 15°

So, ΔPMQ is an isosceles triangle.

Hence,

            MP = MQ = 18

Now, in ΔMRQ

              cos(60°) =

                 =

                RQ = 0.5 × 18

                 RQ = 9

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .