From a boat on the water, the angle of elevation of the drop of a cliff is 31°. From a point 300 m closer, the angle of elevation is 33°. Find the height of the cliff.

the answer should be 2411 m.

I had tan31° = h/x+(x-300)
tan33° = h/x-300 -> (x-300)tan33° = h.

I subbed the first one into the second:
tan31° = (x-300)tan33°/x+x-300

I'm not sure how to go from there or if what I have so far is even right.

To find the height of the cliff, we can use the information given and apply trigonometry.

Let's denote the height of the cliff as 'h' and the distance from the boat to the base of the cliff as 'x'.

Using the given information, we have the following equations:

1) tan(31°) = h / (x + (x - 300))

2) tan(33°) = h / (x - 300)

To solve this problem, we can use the fact that tan(angle) = opposite / adjacent.

Let's rearrange equation 1 to solve for h:

tan(31°) = h / (2x - 300)
h = tan(31°) * (2x - 300)

Now, substitute this expression for h into equation 2:

tan(33°) = (tan(31°) * (2x - 300)) / (x - 300)

Next, we can simplify this equation. Multiply both sides by (x - 300) to get rid of the denominator:

tan(33°) * (x - 300) = tan(31°) * (2x - 300)

Expand the left side:

tan(33°) * x - tan(33°) * 300 = tan(31°) * (2x - 300)

Now, isolate the variable x by moving all terms containing x to one side:

tan(33°) * x - tan(31°) * 2x = tan(33°) * 300 - tan(31°) * 300

Combine x terms:

x * (tan(33°) - tan(31°) * 2) = 300 * (tan(33°) - tan(31°))

Finally, solve for x:

x = (300 * (tan(33°) - tan(31°))) / (tan(33°) - tan(31°) * 2)

Once you have x, substitute it back into the expression for h:

h = tan(31°) * (2x - 300)

Plug in the value of x and calculate h to find the height of the cliff. In this case, the answer should be 2411 m.

From the top* of a cliff, not from the drop of a cliff.