A30m high pole was standing at a point of the length side of a rectangle garden. if the angles of elevation of that pole form end points of that length are found 60 degree and 30 degree, find the length of that garden.

Length of the garden = 69.28 meters.

Step-by-step explanation:

See the attached diagram.

Let CD is the pole with a height of 30 m and the elevation of the top of the pole from the endpoints of the length A and B are 60° and 30° respectively.

So, ∠ DAC = 60° and ∠ DBC = 30°  

Now, Δ ACD is a right triangle and

⇒ meters.

Now, from Δ BCD which is a right triangle,

⇒ meters.

Hence, AB = AC + CB = 17.32 + 51.96 = 69.28 meters. (Answer)

The length of the rectangle garden is 20 i.e 34.64 meters .

Step-by-step explanation:

Given as :

The height of the pole = H = 30 m

The two angles of elevation as 60° and 30°

Let The length of the rectangle garden = L m

Now, From figure

The measure from pole ground to first elevation 60° = x m

The measure from pole ground to second elevation 30° = (L + x ) m

Now, from triangle BOC

Tan Ф =

I.e Tan 60° =

Or, =

or, x =

I.e x = 10 meter      ...1

Again From triangle BAC

Tan Ф =

I.e Tan 30° =

Or, =

Or, L + x = 30 ×   ....2

Put the value of x from  1 into 2

i.e L + 10 meter   = 30 ×

or, L = 30 - 10  

Or, L = 20 = 34.64 meters

I.e length of garden is 20

Hence The length of the rectangle garden is 20 i.e 34.64 meters . answer

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