Question

In Figure 1, PS = 3 cm, QS = 4 cm, ∠PRQ = θ, ∠PSQ = 90°, PQ ⊥ RQ and RQ = 9 cm. Evaluate tan θ.

Answer 1

Given,
PS = 3 cm, QS = 4 cm, RQ = 9cm

In In ΔPSQ,
PQ² =PS² + OS²

PQ² = 3² +4² = 25 

⇒ PQ = 5 cm

In Δ PQR,

tan θ =`"PQ"/"RQ"`
⇒ tan θ =`5/9`