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Question

A contractor plans install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at height of 1.5m and is inclined at an angle of 30o to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60o to the ground. What should be the length of the slide in each case?

A
5m is the length of the slide made for children below the age of 5 years and 3m is the length of the slide made for elder children.
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B
3m is the length of the slide made for children below the age of 5 years and 23m is the length of the slide made for elder children.
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C
7m is the length of the slide made for children below the age of 5 years and 5m is the length of the slide made for elder children.
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D
2m is the length of the slide made for children below the age of 5 years and 72m is the length of the slide made for elder children.
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Solution

The correct option is B 3m is the length of the slide made for children below the age of 5 years and 23m is the length of the slide made for elder children.
In figure, l1 is the length of the slide made for children below the age of 5 years and l2 is the length of the slide made for elder children.
In figure, AB=1.5m,AC=l1m and ACB=30o;PQ=3m;OP=l2m and POQ=60o
ABAC=sin30o and PQOP=sin60o
1.5l1=12 and 3l2=32
l1=2×1.5m and l2=3×23m
l1=3m and l2=23m
222826_236195_ans_3fc49238038f4d02975f0a04deffd836.png

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