Question

in figure 1 ps=3cm,qs=4cm angle PRQ=theeta angle psq=90 degree ,PQ perpendicular to RQ and RQ=9cm Evaluate tan theeta

Answer 1

Answer:

θ = tan ^ -1 (√15/√66)

Step-by-step explanation:

i have attache  Figure Picture You Can   See How Can Solve

QS = 4,  PS=1              suppose PQ=x

Apply pythagoras theorem in angel PQS

   (QS)² = (PQ)² + (PS)²

we can write   4² = x² + 1²

then we solver and get value of x

16 = x² + 1

and finally   x² = 16 - 1   ,      x² = 15

x = √15,     PQ= √15

then

we Apply pythagoras theorem in angel PQS

PQ = √15   ,   PR = y and  RQ = 9

(RQ)² = (PQ)² + (PR)²

9² = (√15)² + y²

then we find value of y like past method

and we get y = √66   ,      PR = √66

we find theeta in angle PRQ

we know tan θ = PQ/PR

sow put value PQ,  PR  And Find Θ

we can write   tan Θ = √15/√66

        Θ = tan^-1 ( √15/√66)