Pls explain 

Asked by praveentripathi999 | 7th Jan, 2020, 04:24: PM

Expert Answer:

A person sees the top of a tree on the bank of a river at an angle of elevation of 70o. Stepping 20 metres back, the angle of elevation becomes 55o. Height of the person is 1.4 m.
We need to draw a rough figure and find:
(i) Height of the tree
(ii) Width of the river
 
L e t space h space b e space t h e space h e i g h t space o f space t h e space t r e e space a n d space x space b e space t h e space w i d t h space o f space t h e space r i v e r
I n space triangle A B C comma
tan space 70 degree equals fraction numerator A B over denominator B C end fraction equals h over x
rightwards double arrow 2.75 equals h over x
rightwards double arrow h equals 2.75 space x

I n space triangle A B D comma
tan space 55 degree equals fraction numerator A B over denominator B D end fraction equals fraction numerator h over denominator x plus 20 end fraction
rightwards double arrow h equals 1.43 open parentheses x plus 20 close parentheses
rightwards double arrow 2.75 space x equals 1.43 open parentheses x plus 20 close parentheses
rightwards double arrow x equals fraction numerator 28.6 over denominator 1.32 end fraction equals 21.7 space
T h e r e f o r e comma space w i d t h space o f space t h e space r i v e r space equals space 21.7 space m
rightwards double arrow h equals 2.75 cross times 21.7 equals 59.6 space m
H e i g h t space o f space t h e space p e r s o n space i s space 1.4 space m
T h e r e f o r e comma space t o t a l space h e i g h t space o f space t h e space t r e e space i s space 59.6 plus 1.4 equals 61 space m

Answered by Renu Varma | 10th Jan, 2020, 10:34: AM