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A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is (SSC CGL 1st Sit. 2013)
- a)65 m
- b)70 m
- c)72 m
- d)60 m
Correct answer is option 'D'. Can you explain this answer?
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A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At...
Given:
- Length of the vertical stick = 12 cm
- Length of the stick's shadow = 8 cm
- Length of the tower's shadow = 40 m
To find:
- Height of the tower
Approach:
- Use the concept of similar triangles to solve the problem.
- Similar triangles have corresponding angles equal and proportional sides.
Solution:
Step 1: Determine the scale factor between the stick and its shadow.
- The stick and its shadow form a right-angled triangle.
- The length of the stick is the height of the triangle, and the length of the shadow is the base.
- Use the formula for the scale factor: scale factor = height/base
Given:
- Height of the stick (h) = 12 cm
- Base of the stick's shadow (b) = 8 cm
Using the formula for the scale factor:
scale factor = height/base
scale factor = 12/8
scale factor = 1.5
Step 2: Determine the height of the tower.
- The tower and its shadow also form a right-angled triangle.
- The length of the tower is the height of the triangle, and the length of the shadow is the base.
- Use the scale factor to find the height of the tower.
Given:
- Base of the tower's shadow (B) = 40 m
- Scale factor (S) = 1.5 (from step 1)
Using the formula for the height:
height = scale factor * base
height = S * B
height = 1.5 * 40
height = 60 m
Therefore, the height of the tower is 60 m.
Answer:
The height of the tower is 60 m.
- Length of the vertical stick = 12 cm
- Length of the stick's shadow = 8 cm
- Length of the tower's shadow = 40 m
To find:
- Height of the tower
Approach:
- Use the concept of similar triangles to solve the problem.
- Similar triangles have corresponding angles equal and proportional sides.
Solution:
Step 1: Determine the scale factor between the stick and its shadow.
- The stick and its shadow form a right-angled triangle.
- The length of the stick is the height of the triangle, and the length of the shadow is the base.
- Use the formula for the scale factor: scale factor = height/base
Given:
- Height of the stick (h) = 12 cm
- Base of the stick's shadow (b) = 8 cm
Using the formula for the scale factor:
scale factor = height/base
scale factor = 12/8
scale factor = 1.5
Step 2: Determine the height of the tower.
- The tower and its shadow also form a right-angled triangle.
- The length of the tower is the height of the triangle, and the length of the shadow is the base.
- Use the scale factor to find the height of the tower.
Given:
- Base of the tower's shadow (B) = 40 m
- Scale factor (S) = 1.5 (from step 1)
Using the formula for the height:
height = scale factor * base
height = S * B
height = 1.5 * 40
height = 60 m
Therefore, the height of the tower is 60 m.
Answer:
The height of the tower is 60 m.
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A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At...
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A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is (SSC CGL 1st Sit. 2013)a)65 mb)70 mc)72 md)60 mCorrect answer is option 'D'. Can you explain this answer?
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