Question

A man on the bank of a river observes that the angle of elevation of top of a tree on the opposite bank is 60. After moving backward 100 m to a point in a
straight line with the tree's foot and his former position, he finds that angle of elevation of top of tree to be 30'. What is the breadth river?
19 20
24 25
Options
29 30
34 35
25 m
50 m
39 40
100
14 45
50/3 m
​

Answer 1

Step-by-step explanation:

Answer

Let AB be the breadth of the river and BC be the height of the tree which makes a ∠ of 60∘ at a point A on the opposite bank. 

Let D be the position of the person after retreating 20 m from the bank. 

Let AB =x metres and BC =h metres.

We know, tan(θ) = Opposite / Adjacent

From right ∠ed △ ABC and DBC,

we have tan60∘=ABBC  and  tan30∘=20+xh

⇒3=xh  and 31=x+20h

⇒h=x3  and h=3x+20

⇒x3=3x+20⇒3x=x+20⇒x=10m

Putting  x=10 in h=3x, we get

h=103=17.32m

Hence, the height of the tree