Question

I’m kinda confused. Can someone help.

Answer 1

PQ =
`PM\cos MPQ + MQ\cos MQP=2PM\cos MQP`

Explanation:

given MQR = 60, PQR = 75

MQP = 75 -60= 15
`QR = ((18(1+\cos 30))^(2)-(2\cos 15)^(2))^{(1)/(2)}`

WE KNOW THAT MQR +QRM +QMR = 180

MPQ = MQP AS ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL

THEREFORE QMR = 90 - 60 = 30

therefore PQM = 75 - 60 = 15

PM = PQ because M is the mid point

therefore PR = PM +
`MQ\cos QMR`

PR =
`18(1+\cos 30)`

`QR = (PR^(2)-PQ^(2)))^{(1)/(2)}`

PQ =
`PM\cos MPQ + MQ\cos MQP=2PM\cos MQP`