Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

The Confederation Bridge joins New Brunswick and Prince Edward Island. From a boat in the Northumberland Strait, the angle of elevation of the highest point on the bridge is 26.6°. When the boat is 100 m closer to the bridge, the angle of elevation is 71.7°. What is the height of the bridge, to the nearest tenth of a metre?

Sagot :

sqdancefan

Answer:

  60.0 m

Step-by-step explanation:

You want the height of a bridge when the angle of elevation to its top is 26.6° from a point, and 71.7° from a point 100 m closer.

Tangent

The tangent relation for sides of a right triangle is ...

  Tan = Opposite/Adjacent

Using the designations in the second attachment, this means ...

  [tex]\tan(26.6^\circ)=\dfrac{HX}{AX}\\\\\\\tan{(71.7^\circ)}=\dfrac{HX}{BX}[/tex]

Solution

We want an expression for the difference AX-BX. Solving each of these equations for AX and BX, we can then solve for HX.

  [tex]AX-BX=\dfrac{HX}{\tan(26.6^\circ)}-\dfrac{HX}{\tan(71.7^\circ)}\\\\\\HX=\dfrac{100\text{ m}}{\dfrac{1}{\tan(26.6^\circ)}-\dfrac{1}{\tan(71.7^\circ)}}\approx60.0\text{ m}[/tex]

The height of the bridge is about 60.0 meters.

View image sqdancefan
View image sqdancefan
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.