To find the height of a pole, a surveyor moves 150 feet away from the base of the pole and then, with a transit 3 feet tall, measures the angle of elevation to the top of the pole to be 26°. what is the height of the pole? round your answer to the nearest foot.

311 ft

73 ft

308 ft

76 ft

reasoning: first you just have to draw a trapezoid with its parallel sides vertical. then make the left vertical side, which will represent the pole. taller than the vertical right side, which will represent the surveyors transit (which is 3 feet, so you have to label the side lengths as 3 feet) the horizontal line segment between the vertical sides has a length of 50 feet. Draw a horizontal line segment from the top of the right vertical side to the left vertical side. the segment that connects the top of the left vertical segment to the right vertical segment is measured at 26° degrees then have the side of the right triangle which has a base angle which is 26° degrees of an angle have length x (ft.).

↓↓↓↓↓(heres my work)↓↓↓↓↓

tan(26°) = x/150  

150 tan(26°) = x  

x ≈ 73.16 ft.  

The length of the pole is 3 feet more than this, so to the nearest foot the pole is 76 ft. high.

HOPE THIS HELPS :)