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USPshnik [31]
2 years ago
8

A suspension bridge has two main towers of equal height. A visitor on a tour ship

Mathematics
1 answer:
Scilla [17]2 years ago
3 0

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 :

<u>In Δ ABC </u>

Tan 42° = \frac{perpendicular}{base}

Or , Tan 42° = \frac{AB}{BC}

Or,  0.900 = \frac{h}{x}

∴ h = 0.900 x

Again :

<u>In Δ ABD </u>

Tan 15° = \frac{perpendicular}{base}

Or , Tan 15° = \frac{AB}{BD}

Or,  0.267 = \frac{h}{( x + 497 )}

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 = \frac{132.699}{0.633}

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

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