A suspension bridge has two main towers of equal height. A visitor on a tour ship
approaching the bridge estimates that the angle of elevation to one of the towers
is 15°. After sailing 497 ft closer he estimates the angle of elevation to the same
tower to be 42° Approximate the height of the tower.

Question

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Respuesta :

WaywardDelaney WaywardDelaney · Answer 1 · 2019-11-15T09:30:45+01:00

Answer:

The Height of the tower is 188.67 ft

Step-by-step explanation:

Given as :

The angle of elevation to tower = 15°

The distance travel closer to tower the elevation changes to 42° = 497 ft

Now, Let the of height of tower = h ft

The distance between 42° and foot of tower = x ft

So, The distance between 15° and foot of tower = ( x + 497 ) ft

So, From figure :

In Δ ABC

Tan 42° = [tex]\frac{perpendicular}{base}[/tex]

Or , Tan 42° = [tex]\frac{AB}{BC}[/tex]

Or, 0.900 = [tex]\frac{h}{x}[/tex]

∴ h = 0.900 x

Again :

In Δ ABD

Tan 15° = [tex]\frac{perpendicular}{base}[/tex]

Or , Tan 15° = [tex]\frac{AB}{BD}[/tex]

Or, 0.267 = [tex]\frac{h}{( x + 497 )}[/tex]

Or, h = ( x + 497 ) × 0.267

So, from above two eq :

0.900 x = ( x + 497 ) × 0.267

Or, 0.900 x - 0.267 x = 497 × 0.267

So, 0.633 x = 132.699

∴ x = [tex]\frac{132.699}{0.633}[/tex]

Or, x = 209.63 ft

So, The height of tower = h = 0.900 × 209.63

Or, h = 188.67 ft

Hence The Height of the tower is 188.67 ft Answer