Question

multiple chice: The line of sight from a small boat to the light at the top of a 35­foot lighthouse built on a cliff 30 feet above the water makes a 35° angle with the water. To the nearest foot, how far is the boat from the cliff? A. 113 feet B. 45 feet C. 93 feet D. 49 feet

Answer 1

The total elevation from the water level to the highest point of the lighthouse is 65 ft. The distance from the cliff to the boat is the side of the triangle that is adjacent to the given angle. The trigonometric equation that would best represent this given is,
                                      tan (35°) = opposite side/adjacent side
                                      tan (35°) = 65 ft / x
The value of x from the generated equation is 92.83 ft. Thus, the answer should be letter C.