Q:

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

Accepted Solution

A:
Answer:The Height of the tower is 188.67 ftStep-by-step explanation:Given as :The angle of elevation to tower = 15° The distance travel closer to tower the elevation changes to 42° = 497 ftNow, Let the of height of tower = h  ftThe distance between 42°  and  foot of tower = x  ftSo, 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 ) × 0.267So, 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 ftHence The Height of the tower is 188.67 ft    Answer