Question

1/ a 13 m long ladder reached a ventilator 12m high from the ground on placing it against a wall at a distance.find the distance of the foot of the ladder from the wall.

2/a tree is broken at a height of 5 M from the ground at is meant so that its top touches the ground at a distance of 12m from the base of the tree.find the orignal height of the tree

Answer 1

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1) ..
GIVEN. :-
HYPOTENUSE , LENGTH OF LADDER = 13m
PERPENDICULAR, HEIGHT OF WALL= 12m
BASE = ?
TO FIND :-
the distance of the foot of the ladder from the wall.


Solution :-
1) the ladder, wall and distance btw their foots make a right angled triangle, so applying Pythagoras theorm....
→hypotenuse ^ 2 = perpendicular ^2 + base^2
→13^2 = 12^2+ base ^ 2
→√169-144 = base
→√25 =base
→5m = base, the distance of the foot of the ladder from the wall.



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2)....
GIVEN :-
HYPOTENUSE = ?
BASE = 12m (a distance from the base of the tree)
perpendicular = 5m (tree is broken at a height of 5 M from the ground)

TO FIND :-
the orignal height of the tree

SOLUTION:-
the tree's broken part, remained 5m part and distance between them of 12 m forms a right angled triangle, so applying Pythagoras theorm.

→hypotenuse ^ 2 = perpendicular ^2 + base^2
→hypotenuse ^ 2 = 5^2 +12^2
→hypotenuse ^ 2 = 25+144
→hypotenuse ^ 2 =169
→hypotenuse= √169
→hypotenuse= 13 m


so original length or height of tree = broken part's length+ remained part's length
original length or height of tree = 13+5
original length or height of tree = 18m

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