From The Bridge Of A Boat On The Niagara River
Questions about trigonometry? 3
From the deck of the boat on the Niagara River, the peak angle of the rope waterfall is 64 degrees. The angle of inclination at the bottom of the case is 6 degrees. When the deck of a boat is three feet above the water, calculate the height of the fall.
x = Distance between boat and waterfall (horizontal)
z = height from the bridge of the boat to the top of the waterfall
The answer is: z + 2.8
We know
6 = 2.8 / x
x = 2.8 / 6
64 = z / x
z = x * 64
z = 2.8 * 64/6
z = 2.8 * 2.0503 / 0.1051
z = 54.6 meters
Falling height = 54.6 + 2.8 = 57.4 meters.
Sketch without working for you. It will be a triangle, from the deck of the boat to the bottom of the waterfall, from the bottom of the waterfall to the top of the waterfall, and from the top of the waterfall to the deck of the boat. Now add a horizontal line from the deck of the ship to the waterfall line. Now you have two right triangles. First calculate the length of this new line, then use that length to determine the height of the cut relative to the line you just added. That number plus 2.8 is the height of the fall.
