To find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit 8 feet tall, measures the angle of elevation to the top of the pole to be 26. to the nearest foot, what is the height of the pole
Refer to the figure. Let AB be the height of the pole; CD be the height of the transit; BC is the distance from the base of the pole to the transit.
Triangle ADE is a right triangle with angle D measuring 26 degrees. Using the tangent function, we have [tex]tan\:26^{\circ} =\frac{AE}{120}[/tex] So, [tex]AE=120\:tan\:26^{\circ} [/tex] [tex]AE=58.53\:[/tex]
Therefore, the overall height of the pole is [tex]AB=58.53+8=66.53\:feet[/tex]
