Question

Given: ∆PQR, m∠R = 90° m∠PQR = 75° M ∈ PR , MP = 18 m∠MQR = 60° Find: RQ

Answer 1

Answer: RQ= 8.99 ( approx)

Explanation:

Let MR= x

Since, In triangle, PRQ, tan 75°=
`(18+x)/(RQ)`

⇒ RQ=
`(18+x)/(tan 75^(\circ))`

Now, In triangle MRQ,

tan 60°=
`(18+x)/(RQ)`

⇒ RQ=
`(x)/(tan 60^(\circ))`

On equating both values of RQ,

`(18+x)/(tan 75^(\circ))=(x)/(tan 60^(\circ))`

⇒
`(18+x)/(x)=(tan 75^(\circ))/(tan 60^(\circ))`

⇒
`(18+x)/(x)=(tan 75^(\circ))/(tan 60^(\circ))`

⇒
`(18+x)/(x)=2.15470053838`

⇒
`18=2.15470053838x-x`

⇒
`x=15.5884572681`≈15.60

Thus RQ=8.99999999999≈8.99