What should be the height of a flag where a 20 feet long ladder reaches 20 feet below the flag (The angle of elevation of the top of the flag at the foot of the ladder is `60^(@)`) ?

Options

A. 20 feet
B. 30 feet
C. 40 feet
D. `20 sqrt(2)` feet

Answer

B

Explanation

In `DeltaABD`,
`tan 60^(@)=(BD)/(AB)`
`rArr sqrt(3)=(h)/(AB)`
`rArr AB=(h)/(sqrt(3))`

`rArr AB=(h)/(3) sqrt(3)`
Now, in `Delta ABC`
`AC^(2)=AB^(2)+BC^(2)`
`rArr 20^(2)=((h)/(sqrt(2)))^(2)+(h-20)^(2)`
`rArr h^(2)+3h^(2)-120h=0`
`rArr 4h^(2)-120h=0`
`rArr h(h-30)=0`
h=0 or 30
h=0 not possible
`rArr h = 30 ft`