Question

A and B are standing on the opposite banks of a river facing the river (not directly opposite
each other in the bank
slightly to his right, along laline making an angle of 60° with the bank of the river. B observes a tower on the bank
Where A is standing) to his left along a line making an angle of 30° with the bank of the river. If the width of the river
is 80m, How far is A from the tower?
An observer, 1.5 m tall, is 28.5 m away from a tower 39 m hinh Datorming the

Answer 1

Answer:

Let CD=h be the height of the tree and BC=x be the breadth of the river.

From the figure ∠DAC=30∘ and ∠DBC=60∘

In right angled triangle △BCD,tan60∘=BCDC

⇒3=xh

⇒h=x3      .(1)

From the right-angled triangle △ACD

tan30∘=40+xh

⇒31=40+xh

⇒3h=40+x      2)

From (1) and (2) we have

3(x3)=40+x

⇒3x=40+x

⇒3x−x=40

⇒2x=40