Question

12. Two pillars of equal height stand on either side of a road which is 40 m wide. From a point on the road
between the pillars, the angles of elevation of tops of the pillars are 30° and 60°. Find
(i) the position of the point of the point on the road, and
(ii) the height of each pillar.​

Answer 1

Answer:

hope it helps you!!!!

Step-by-step explanation:

Let AB and CD be two pillars of equal heights, say, h metres. Let P be a point on road such that AP= x m and PC = 100 -x. APB= 600 and CPD =300.

In right ∆PAB,

Tan60 =  

……….. (1)

In right ∆PCD,

tan30 =  

…………….(2)

From (1) and (2) we get,

3x=100-x or x=25

From (1) , h=25

Thus, the height of the pillars is 25 metres.

OR

Let A and B be the two positions of the ship. Let d be the distance travelled by the ship during the period of observation, i.e., AB=d metres.

Suppose that the observer is at the point P.

Given that PC = 100m.

Let h be the distance (in metres) from B to C.

From right triangle PCA, we have

d+h = 100 ..(i)

Again in triangle PCB, we have,

h =  metres. Putting the value of h in (i) we get,

d= 100  =  = 115.47 (approx.)

Thus, the distance travelled by the ship from A to B is 115.47 m(approx.