Question

The angle of elevation of the top of the building from a point
on the ground which is 50 metres away from the foot of the
tower is 60°. Find the height of the tower? please tell me fast
​

Answer 1

Answer :-

• The height of the tower is 50√3 m.

Step-by-step explanation:

To Find:-

• The height of the tower.

Solution:

Given that,

• The angle of elevation of the top of the building from a point on the ground which is 50m away from the foot of the tower is 60°

Let us consider AB be the top of the building and C be the point of observation.

∴ BC = 50m

As, angle of elevation is 60°

∴ ∠ACB = 60°

Figure,

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf ?}\put(2.8,.3){\large\bf 50 \: m}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf {60}^{\circ} }\end{picture}$

And in ∆ ABC,

⇒ AB/50 = tan 60°

⇒ AB/50 = √3

⇒ AB = 50 × √3

⇒ AB = 50√3

Hence, The height of the tower is 50√3 metres.

Answer 2

Given :-

• Angle of elevation = 60°
• Distance of building from a point on ground = 50m

To find :-

• Height of tower.

Solution :-

In a triangle PQR :-

• PQ = x
• QR = 50 m
• Q = 90°
• R = 60°

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ tan = Perpendicular / base

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎=> tan 60° = x / 50

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎tan 60° = √3

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎=> √3 = x / 50

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎=> x = 50√3

Hence, height of tower = 50√3 m.

ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎