Question

Rohini saw an eagle on the top of a tree at an angle of elevation Of 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 4m. While observing the eagle from there the angle of elevation was 52. At what height from the ground was the eagle? Give Your answer up to nearest integer. (tan 61 =1.80, Tan52 = 1.28 , tan29 = 0.55 , tan 38 = 0.78)

Answer 1

$\huge\bf{\red{\underline{\underline{Solution:-}}}}$

In the figure,

seg AB represents the tree

seg CD represents the house

A is the positions of the eagle.

D is the point of observation of Rohini while standing the door of the house.

C is the point if observation of Rohini from the terrace

<ACE and < ADB are the angels of elevation.

CD = 4 m, < ACE = 52 degree & < ADB = 61 degree

☐CDBE is a rectangle

⛬ BE = CD = 4 m........... [Opposite sides of rectangle are equal ]

Let AE be x m .

AB = AE + EB....... [A - E - B]

⛬ AB = ( x + 4)m.

In right angled ABD,

$\bf{tan61 = \frac{AB}{BD}}$.......[By defination ]

$\bf\therefore{1.80 = \frac{x + 4}{BD}}$....(tan61 = 1.80)

$\bf{BD = \frac{x + 4}{1.80}m}$

CE = BD...[Opposite sides of a rectangle of equal]

$\bf{CE = \frac{x + 4}{1.80}m}$

In right angled AEC,

$\bf{tan52 = \frac{AE}{CE}}$..[By defination ]

$\bf{ 1.28 = \frac{x}{x + 4}\frac{1}{1.80}}$... (tan52= 1.28)

$\bf{ 1.28 = \frac{1.80x}{x + 4}}$

⛬ 1.28 (x + 4) = 1.80x

⛬ 1.28x + 5.12 = 1.80x

⛬ 1.80x - 1.28x = 5.12

⛬ 0.52x = 5.12

⛬ ${x = \frac{5.12}{0.52}}$

⛬ x = 9.846

⛬ x = 10.......(to the nearest integer)

⛬ AB = AE + EB.... (A - E - B)

⛬ AB = x + 4

⛬ AB = 10 + 4

⛬ AB = 14 m

The eagle was at a height 14 m. From the ground.

$\bf{\red{\underline{\underline{MuskaŊ}}}}$

Answer 2

Answer:

13.77 m

Step-by-step explanation:

Define x and y:

Let x be the height from the ground to the eagle

Let y be the ground distance from the door to the tree

Find the distance when she was at the door:

tanθ = opp/adj

tan(61) = x/y

y = x/tan(61)

Find the distance when she was at the terrace:

tanθ = opp/adj

tan(52) = (x - 4)/y

y = (x- 4)/tan(52)

Solve x:

Both the distance are equal

x/tan(61) = (x- 4)/tan(52)

x tan(52) = (x - 4)tan (61)

x tan (52) = x tan(61) - 4 tan(61)

x tan(61) - x tan(52) = 4 tan(61)

x( tan(61) - tan(52)) = 4 tan(61)

x = 4 tan(61) ÷ ( tan(61) - tan(52) ) = 13.77 m

Answer: The height of the eagle from the ground is  13.77 m