Question

Inner part of a cupboard is in the cubiodical shape with its length,breadth and height in the ratio of 1:root2:1. What is the angle made by the longest stick which can be inserted cupboard with its base inside.

Answer 1

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:w:h=1:√2:1

Therefore,

Let us say

Length, l = 1

Width, w = √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,

tanø=height of the cupboard /

diagonals of the base of the

cup board

So,

tanø= 1/diagonals of the base of

the cup board

Now,

Diagonal of the base of the cupboard is given by,

Diagonals of base=√l^2+b^2

=√1^2+(√2)^2

=√3

So,

Angle is,

tanø= 1/√3

tan30°=1/√3

So ø=30°

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