Question

if angle of depression of Point When observed from P is 30 degre. If Pq =5m and and angle PQR=90 degree then QR will be​

Answer 1

Step-by-step explanation:

Let height of tower MN is h

In ΔQMN 

QMMN=tan 30°

∴QM=3h=MR ..........(1)

Now in ΔMNP

MN=PM .........(2)

In ΔPMQ

MP=(200)2−(3h)2

∴ From (2)

(200)2−(3h)2=h⇒h=100m

Hope it is helpful

Answer 2

Step-by-step explanation:

Given;

For a right angle triangle PQRPQR , \angle P=60∠P=60 °,\angle R=30∠R=30 ° and PR=12unitsPR=12units

∴\angle Q=90∠Q=90 ° (∵ \bigtriangleup PQR△PQR is right angle triangle)

From figure,

sin30=\frac{PQ}{PR}sin30=

PR

PQ

⇒PQ=\frac{1}{2}\times 12PQ=

2

1

×12

∴PQ=6unitsPQ=6units

And,

tan30=\frac{PQ}{QR}tan30=

QR

PQ

⇒QR=\frac{6}{\frac{1}{\sqrt{3} } }QR=

3

1

6

∴QR=6\sqrt{3} unitsQR=6

3

units

So, the value of PQPQ and QRQR are 6units6units and 6\sqrt{3} units6

3

units