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)

Step-by-step explanation:

Let MR= x

Since, In triangle, PRQ, tan 75°= $\frac{18+x}{RQ}$

⇒ RQ=  $\frac{18+x}{tan 75^{\circ}}$

Now, In triangle MRQ,

tan 60°= $\frac{18+x}{RQ}$

⇒ RQ=  $\frac{x}{tan 60^{\circ}}$

On equating both values of RQ,

$\frac{18+x}{tan 75^{\circ}}=\frac{x}{tan 60^{\circ}}$

⇒$\frac{18+x}{x}=\frac{tan 75^{\circ}}{tan 60^{\circ}}$

⇒$\frac{18+x}{x}=\frac{tan 75^{\circ}}{tan 60^{\circ}}$

⇒$\frac{18+x}{x}=2.15470053838$

⇒$18=2.15470053838x-x$

⇒$x=15.5884572681$≈15.60

Thus RQ=8.99999999999≈8.99