Question

a flagstaff stands on the top of a 12 m high tower. from a point on the ground the angles of elevation of the top and bottom of the flagstaff are observed to be 45° and 30° respectively. find the height of the flagstaff (
$\sqrt{3 } = 1.73$

Answer 1

Answer:

Step-by-step explanation: right answer and see this its not wrong

Answer 2

Answer:

The height of the flagstaff is 26.04 m

Step-by-step explanation:

The height of the tower $(AC) = 12\text{ m}$

Consider the height of the flagstaff =  $(CD) = h\text{ m}$

Total height of the flag top from the ground  $(AD) = (12+h)\text{ m}$

The distance between the flag post and the point (B) =$(AB) =x\text{ m}$

In $\Delta ABC$ is a right angle triangle and $\angle ABC=30^{\circ}$

therefore,

$\frac{AC}{AB}=tan45^{\circ}\\\\\Rightarrow{AC}=AB\\\\\Rightarrow{12}=x\\\\\Rightarrow{x}=12$

In $\Delta ABD$ is a right angle triangle and $\angle ABD=30^{\circ}$

therefore,

$\frac{AD}{AB}=tan30^{\circ}\\\\\Rightarrow{AD}=\sqrt{3}\times{AB}\\\\\Rightarrow{h+12}=\sqrt{3}\times12\\\\\Rightarrow{h+12}=3.17\times12\\\\\Rightarrow{h+12}=38.04\\\\\Rightarrow{h}=38.04-12\\\\\Rightarrow{h}=26.04\text{ m}$

Therefore, the height of the flagstaff is 26.04 m