Question

Inner part of a cupboard is in the cuboidal shape with its length, breadth and height in the ratio 1 : √2 : 1. What is the angle made by the longest stick which can be inserted cupboard with its base inside.

Answer 1

Answer:

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Answer 2

Answer:

Angle made by the stick with the base is 30 degrees.

Step-by-step explanation:

In the given question,

We have the ratio of the length to the width and to the height of the cupboard.

So,

$l:b:h=1:\sqrt{2}:1$

Therefore,

Let us say

Length, l = 1

Width, w = $\sqrt{2}$

Height, h = 1

Now,

We know that longest stick will be along the body diagonal of the cupboard.

Therefore,

Angle made by the longest stick with the base of the cupboard is given by,

$tan\theta =\frac{Height\ of\ the\ cupboard}{Diagonal\ of\ the\ base\ of\ cupboard} \\So,\\tan\theta =\frac{1}{Diagonal\ of\ the\ base\ of\ cupboard}$

Now,

Diagonal of the base of the cupboard is given by,

$Diagonal\ of\ the\ base=\sqrt{l^{2}+b^{2}} =\sqrt{(1)^{2}+(\sqrt{2} )^{2}} =\sqrt{3}$

So,

Angle is,

$tan\theta=\frac{1}{\sqrt{3} } \\So,\\\theta=30 \ degree$

Therefore, the angle made by the stick with the base is 30 degrees.