A communication tower is 34m tall. Jane stands somewhere in front of the tower to the right and measures the angle of elevation to be 70 degrees. Bill stands somewhere in front of the tower to the left and measures the angle of elevation to be 50 degrees. How far apart are Jane and Bill if the angle between Jane, the base of the tower and bill is 90 degrees. Round to the nearest meter.

Question

A communication tower is 34m tall.  Jane stands somewhere in front of the tower to the right and measures the angle of elevation to be 70 degrees.  Bill stands somewhere in front of the tower to the left and measures the angle of elevation to be 50 degrees.  How far apart are Jane and Bill if the angle between Jane, the base of the tower and bill is 90 degrees.  Round to the nearest meter.

Henry · Answer

Tan70 = 34/d1, d1 = 34/Tan70 = 12.4 m. = Jane's distance from the tower. Tan50 = 34/d2, d2 = 34/Tan50 = 28.5 m. = Bill's distance from the tower. d1+d2 = 12.4 + 28.5 = 40.9 m. Apart.