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EXTREMELY URGENT!!! The angles of elevation of the top of two vertical towers as seen from the
middle point of the lines joining the foot of the towers are 45° & 60°. The ratio of the height of the towers is:

Respuesta :

oladayoademosu

Since the angles of elevation of the top of two vertical towers is 45° & 60°, the ratio of the height of the towers is 0.58:1

How to find the ratio of the height of the towers

Since the angles of elevation of the top of two vertical towers as seen from the middle point of the lines joining the foot of the towers are 45° & 60°.

The height of the tower, the line of sight and the ground form a right angled trangle

Height of first tower

Let

  • h = height of first tower,
  • d = distance of tower to middle point = L/2 where L = distance between tower and
  • Ф = angle of elevation of tower from midpoint = 45°

Using trigonometric ratios, we have that

tanФ = h/d

= h/L/2

= 2h/L

So, h = LtanФ/2

= Ltan45°/2

= L/2 × 1

= L/2

Height of second tower

Let

  • h' = height of first tower,
  • d = distance of tower to middle point = L/2 where L = distance between tower and
  • Ф' = angle of elevation of tower from midpoint = 60°

Using trigonometric ratios, we have that

tanФ' = h'/d

= h'/L/2

= 2h'/L

So, h' = LtanФ'/2

= Ltan60°/2

= L/2 × √3

= √3L/2

Ratio of the height of the towers

So, the ratio of the height of the towers is n = h/h'

= L/2 ÷ √3L/2

= 1/√3

= 1/1.732

= 0.577

≅ 0.58

So, the ratio of the height of the towers is 0.58:1

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