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AN ARCHER CLIMBS TO THE TOP OF A 10m HIGH BUILDING AND AIMS AT A BIRD A TOP OF A TREE 17m AWAY. THE LINE OF SIGHT FROM THE ARCHER TO THE BIRD MAKES AN ANGLE OF 45° TO THE HORIZONTAL. WHAT IS THE HEIGHT OF THE TREE...?
Answers
Hey MATE
ANSWER:-
given :-archer climbs 10m
bird on tree 17m away
bird makes an angle of 45°
10 +45 as given in the question
=55
Therefore the height of the tree is 55 m
hope it helps you .
Given : An Archer climbs to the top of a 10m high building and aims at a bird on top of tree 17m away.
The line of sight from the Archer to the bird makes an angle of 45° to the horizontal.
To Find : What is the height of tree?
Solution:
Height of tree = h m
height of tree above building = h - 10 m
Bird 17 m away
Hypotenuse = 17 m
Angle = 45°
Sin 45° = ( h - 10)/17
=> 1/√2 = ( h - 10)/17
=> h = 10 + 17/ √2
height of tree = 10 + 17/ √2 m
Height of tree = h m
height of tree above building = h - 10 m
if tree 17 m away
Base = 17 m
Angle = 45°
tan 45° = ( h - 10)/17
=> 1 = ( h - 10)/17
=> h = 27
height of tree = 27 m
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