Question

P is equals to 3 cm qr is equal to 4 cm angle prq = 2 theta angle psq equals to 90 degree pq perpendicular to

Answer 1

Answer:

The value of tanθ is \frac{5}{9}

9

5

.

Step-by-step explanation:

From the figure it is clear that

\angle PSQ=90^{\circ}∠PSQ=90

∘

It means triangle PSQ is a right angled triangle.

Using Pythagoras theorem in triangle PQS, we get

hypotenuse^2=base^2+perpendicular^2hypotenuse

2

=base

2

+perpendicular

2

PQ^2=PS^2+QS^2PQ

2

=PS

2

+QS

2

PQ^2=3^2+4^2PQ

2

=3

2

+4

2

PQ^2=25PQ

2

=25

PQ=5PQ=5

The length of PQ is 5 cm.

\angle PQR=90^{\circ}∠PQR=90

∘

It means triangle PQR is a right angled triangle. In a right angle triangle

\tan \theta=\frac{perpendicular}{base}tanθ=

base

perpendicular

\tan \theta=\frac{PQ}{QR}tanθ=

QR

PQ

\tan \theta=\frac{5}{9}tanθ=

9

5

Therefore the value of tanθ is \frac{5}{9}

9

5

.