Question

roshni saw an eagle on the top pf a tree at an angle of elevation 61°,while she was standing at the door of her house.She went on the terrace of the house so that she could see it clearly.The terrace was at a height of 4 m.While observing the eagle from there the angle of elevation was 52°.At what height from the ground was the eagle? give your answer upto nearest integer ( tan61°=1.80,tan52°=1.28,tan29°=0.55,tan38°=0.78)

Answer 1

Answer:13.84m

Step-by-step explanation:

Please see the attached file.

Answer 2

Answer:

Step-by-step explanation:

Height of the Building $AD=4\text{ m}$

Consider the Horizontal distance between the House and the tree $AB=x\text{ m}$

Height of the eagle from the ground $BC=y\text{ m}$

$\angle BAC=61^{\circ}$ and $\angle EDC=52^{\circ}  </p><p>therefore,</p><p>In [tex]\Delta ABC$

$\frac{BC}{AB}=tan61^{\circ}\\\\\Rightarrow\frac{y}{x}=1.80\\\\\Rightarrow{x}=\frac{y}{1.80}\\\\\Rightarrow{x}=\frac{10y}{18}\text{.............equation-1}$

In $\Delta DEC$

$\frac{CE}{DE}=tan52^{\circ}\\\\\Rightarrow\frac{y-4}{x}=1.28\\\\\Rightarrow{x}=\frac{y-4}{1.28}\\\\\Rightarrow{x}=\frac{100(y-4)}{128}\text{.............equation-2}$

Now comparing both equation we get

$\frac{10y}{18}=\frac{100(y-4)}{128}\\\\\Rightarrow\frac{y}{18}=\frac{(10y-40)}{128}\\\\\Rightarrow128y=180y-720\\\\\Rightarrow180y-128y=720\\\\\Rightarrow52y=720\\\\\Rightarrow{y}=\frac{720}{52}\\\\\Rightarrow{y}=13.84$

The height of the eagle from the ground was =13.84 m