Trigonometry Question ?

Question

From the bridge of a boat on the Niagara River, the angle of elevation of the top of the Horseshoe Falls is 64degrees. The angle of depression of the bottom of the Falls is 6 degrees. If the bridge of the boat is 2.8 m above the water, calculate the height of the Horseshoe Falls.

Answer 1

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x = the distance between the boat and the falls (horizontally)

z = the height from the bridge of the boat to the top of the falls

answer will be : z + 2.8

We know

tang6 = 2.8 / x

x = 2.8 / tang6

tang64 = z / x

z = x*tang64

z = 2.8 * tang64 / tang6

z = 2.8 * 2.0503 / 0.1051

z = 54.6 m

Height of the falls = 54.6 + 2.8 = 57.4 m.

Answer 2

Without doing your homework for you, draw out the diagram. It'll be a triangle from the bridge of the boat to the base of falls, the base of the falls to the top of the falls, and the top of the falls to the bridge of the boat. Now add a horizontal line from bridge of the boat to the line of the falls. You now have two right triangles. First solve for the length of this new line, then use that length to solve for the height of the falls above the line you just added. That number plus the 2.8 is the height of the falls.