Question

From the top of a building 15 m high the angle of elevation of the top of a
tower is found to be 30. From the bottom of the same building the angle of
elevation of the top of the tower is found to be 60°. Find the height of the
tower and the distance between the tower and building.​

Answer 1

Answer:

Here,                                                                                              

AB = height of the tower

CD = height of building

DB= distance between tower and building

The line CE is just imaginary

Now,

CD=EB=15m (being the opposite sides of rectangle DCBE)

<ADB=600  

EB (Perpendicular) =15m

DB =? (We need to find this distance as it is mentioned in question)

Tan600 =p/b

Or, √3 = 15/b    (the value of tan 60 is root 3 and we used tan because wee neeed to find b and we have p)

Or, b√3 = 15

Or, b = 15 / √3

Therefore b = 8.67 m  

So, the distance between the tower and building is 8.67m  

Now, DB=CE=8.67 m  

AE( Perpendicular ) =?(we need to find this)

<ACE = 300

CE=8.67 m

Now,

Tan30 = p/b

1/√3 = p / 8.67

Or, 8.66/√3 = p

There fore p=5 ( the answer is 4.99 but it is 5m)

Total height = AE + EB = 5 + 15 = 20m

Step-by-step explanation: