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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
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