Question

A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet. Find the length of the side of the lot opposite the 60° angle.  

Answer 1

THERE ARE TWO special triangles in trigonometry. One is the 30°-60°-90° triangle. The other is the isosceles right triangle. They are special because, with simple geometry, we can know the ratios of their sides. In a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : . Note that the smallest side, 1, is opposite the smallest angle, 30°; while the largest side, 2, is opposite the largest angle, 90°. And  sqrt(3) is opposite to 60°

Let x be the side opposite to 60

(x/41)= sqrt(3) /1

X = 71.01 ft