Question

a diagonal of rectangle forms a 30 degree angle with each of the longer sides of the rectangle. if the length of the shorter side is 3, what is the length of the diagonal

Answer 1

Length of diagonal = 6

Explanation:

Given that

Diagonal of a rectangle makes an angle of
`30^\circ` with the longer side.

Kindly refer to the attached diagram of the rectangle ABCD such that diagonal BD makes angles of
`30^\circ` with the longer side CD and BA.

`\angle CDB =\angle DBA =30^\circ`

Side AD = BC = 3 units

To find:

Length of diagonal BD = ?

Solution:

We can use the trigonometric ratio to find the diagonal in the
`\triangle BCD` because
`\angle C =90^\circ`

Using the sine :

`sin\theta = (Perpendicular )/(Hypotenuse )`

`sin\angle CDB = (BC)/(BD)\\\Rightarrow sin30^\circ = (3)/(BD)\\\Rightarrow \frac{1}2 = (3)/(BD)\\\Rightarrow BD =2 * 3 \\\Rightarrow BD = \bold{6 }`

So, the answer is:

Length of diagonal = 6