At a point on level ground, the angle of elevation of a vertical tower is found to be - Maths - Some Applications of Trigonometry

Question

At a point on level ground, the angle of elevation of a
vertical tower is found to be such
that its tangent is 5/12
On walking 192m towards the tower, the tangent of the angle
of
elevation is 3/4
Find the height of the tower

Devanshi Modha · Answer

<img width="449"
height="295" src=
"file:///C:DOCUME~1naidehiLOCALS~1Tempmsohtml101clip_image002%20jpg"
v:shapes="_x0000_i1025" alt="">
let height of the tower b h
tan theta = 5/12
h /192 + x = 5/12
12h = 5(192 + x)
12h = 960 + 5x
x = -960 + 12h/5 __ 1
tan phi = h/x
3/4 = h/x
x = 4h / 3 _____2
1 = 2
-960+12h/5 = 4h/3
3(-960 + 12h) = 20h
-2880 + 36h = 20h
2880 = 16h
Therefore h = 2880 / 16 = 180
m

At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192m towards the tower, the tangent of the angle of . elevation is 3/4. .Find the height of the tower.

At a point on level ground, the angle of elevation of a vertical tower is found to be such

that its tangent is 5/12.

On walking 192m towards the tower, the tangent of the angle of .

elevation is 3/4.

.Find the height of the tower.