A television antenna stands on the edge of the top on a 19 story building. From a point 312 ft. from the base of the building, the angle of the elevation to the top of the antenna is 51 degrees. If each story is 12 feet high find the height of the antenna.
312 ft is leg one of a right triangle;
(height of building + height of antenna) is leg two
angle A is 51 degrees
(height of building + height of antenna) / 312 ft = tan A
(height of building + height of antenna) = (tan A) * 312 ft
(height of building + height of antenna) = 1.2349 * 312 ft
(height of building + height of antenna) = 385.2888 ft
height of building = 19 stories * 12 ft / story = 228 ft
228 ft + (height of antenna) = 385.2888 ft
height of antenna = 385.2888 ft - 228 ft = 157.2888 ft
The antenna is 157.2888 ft high