A 30m 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.
Accepted Solution
A:
Answer: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 [tex]\tan 60 = \frac{CD}{AC}[/tex]
⇒ [tex]AC = \frac{CD}{\tan 60} = \frac{30}{\tan 60} = 17.32[/tex] meters.
Now, from Δ BCD which is a right triangle, [tex]\tan 30 = \frac{CD}{CB}[/tex]
⇒ [tex]CB = \frac{30}{\tan 30} = 51.96[/tex] meters.
Hence, AB = AC + CB = 17.32 + 51.96 = 69.28 meters. (Answer)