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.
