Answer
The height of the building is 218.1 ft
Work Step by Step
Let $d$ be the horizontal distance from the building to the point of observation on the ground. Let $x$ be the height of the building.
We can use the law of sines and the angle to the bottom of the flagpole to find an expression for $d$:
$\frac{d}{sin(90^{\circ}-26.0^{\circ})} = \frac{x}{sin(26.0^{\circ})}$
$d = \frac{x~sin(64.0^{\circ})}{sin(26.0^{\circ})}$
We can use the law of sines and the angle to the top of the flagpole to find an expression for $d$:
$\frac{d}{sin(90^{\circ}-35.0^{\circ})} = \frac{x+95.0}{sin(35.0^{\circ})}$
$d = \frac{(x+95.0)~sin(55.0^{\circ})}{sin(35.0^{\circ})}$
We can equate the two expressions for $d$ and solve for $x$:
$\frac{x~sin(64.0^{\circ})}{sin(26.0^{\circ})} = \frac{(x+95.0)~sin(55.0^{\circ})}{sin(35.0^{\circ})}$
$x~sin(64.0^{\circ})~{sin(35.0^{\circ}) = (x+95.0)~sin(55.0^{\circ})~sin(26.0^{\circ})}$
$0.515527~x = 0.359093~(x+95.0)$
$0.1564~x = 34.114$
$x = \frac{34.114}{0.1564}$
$x = 218.1~ft$
The height of the building is 218.1 ft
