Question

the angle of elevation of top Q of a vertical tower pq from x on the ground is 60 degree. At a point Y , 40 m vertically above X the angle of elevation is 45 degree .Find the height of the tower pq and the distance XQ. . ​

Answer 1

Answer:

Step-by-step explanation:

In triangle YRQ,

tan 45 = QR/ YR

This gives YR = x

or XP = x [ As YR = XP ] ...... (1)

Now, in triangle XPQ,

tan 60 = PQ / PX

V3 = x+40/x      [Using(1)]

This gives:

x = 40 / V3 - 1

x = 20 (V3 + 1) = 54.64 m

(By rationalisation)

So, height of the tower, PQ = x + 40 = 54.64 + 40 = 94.64 m

 

In triangle XPQ,

sin 60 = PQ / XQ

V3/2 = 94.64/ XQ

This gives XQ = 109.3 m