The mathematics teacher took the class to the playground. She wanted to show how to calculate
the height of the palm tree. She asked one of the students to stand in front of the tree. The sun shines
down at the same angle on both the tree and the student. Shadows are formed for both of these
objects. By comparing the two shadows, against the two heights and using the concept of similar
triangles, one can work out the unknown height of the tree.
The height of the palm tree in the given figure is
(i) 18 m (ii) 12 m (iii) 13.5 m (iv) 10.5 m
1M
b) The distance between the boy and the palm tree is
(i) 12 m (ii) 13.5 m (iii) 10.5 m (iv) 14 m
1M
c) If the angle of elevation of the sun decreases, then the length of the shadow of the boy
(i) may or may not change (ii) will increase (iii) will decrease (iv) will not change
1M
d) If two sides of one triangle are proportional to two corresponding sides of another triangle, and their
corresponding included angle are congruent: then the two triangles are
(i) always similar (ii) congruent (iii) not always similar (iv) never similar
1M
e) If two triangles have proportional sides, they are
(i) always similar (ii) congruent (iii) not always similar (iv) never similar
Answers
Given : The mathematics teacher took the class to the playground. She wanted to show how to calculate the height of the palm tree.
To Find : The height of the palm tree in the given figure is
(i) 18 m (ii) 12 m (iii) 13.5 m (iv) 10.5 m
b) The distance between the boy and the palm tree is
(i) 12 m (ii) 13.5 m (iii) 10.5 m (iv) 14 m
c) If the angle of elevation of the sun decreases, then the length of the shadow of the boy
(i) may or may not change (ii) will increase (iii) will decrease (iv) will not change
Solution:
Height of boy/Shadow of boy = Height of tree / Shadow of tree
=> 1.5/1.5 = h/12
=> 1 = h/12
=> h = 12
Height of tree = 12 m
The distance between the boy and the palm tree
= 12 - 1.5
= 10.5 m
angle of elevation of the sun decreases then the length of the shadow of the boy will increase
If two sides of one triangle are proportional to two corresponding sides of another triangle, and their
corresponding included angle are congruent: then the two triangles are
(i) always similar
If two triangles have proportional sides, they are
(i) always similar
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