how does i knot = 1 nautical mile per hour figure into the calculation of this problem

Question

From a ship off-shore, the angle of elevation of a hill is 1.1 degrees. After the ship moves inland at 4.5 knots for 20 MINUTES, the angle of elevation is 1.4 degrees. How high is the hill? the answer is 817 feet

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Answer 1

Since 20 minutes is 1/3 of an hour, the ship will have travelled 1/3 of 4.5 nautical miles in that 20 minutes or 1.5 nautical miles. Since the answer is in feet convert 1.5 nautical miles to feel. A nautical mile is about 6076 feet. That means the ship has travelled about 9114 feet in that 20 minutes.

Now you are able to create two right triangles. Let x = distance from the ship to the shore after the 20 minutes.

Let h = height of the hill.

tan(1.1) = h/(x + 9114)

tan(1.4) = h/x

Two equations with two unknowns allows you to use the substitution method to solve for x and h (focus on h).

I would solve the 2nd equation for x and substitute into the 1st equation.

tan(1.1) = h/[h/tan(1.4) +9114]

htan(1.1)/tan(1.4) + 9114tan(1.1) = h

Multiply through by tan(1.4) to clear fraction:

htan(1.1) + 9114tan(1.1)tan(1.4) = h tan(1.4)

9114tan(1.1)tan(1.4) = htan(1.4) - htan(1.1)

h = 9114tan(1.1)tan(1.4) / [tan(1.4) - tan(1.1)]