A boat is 144 feet from the base of cliff. If the distance from the top of the cliff to the boat is 36 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a foot if necessary.

Step 1 ：Given that the distance from the boat to the base of the cliff is 144 feet, we denote this as \(a = 144\).

Step 2 ：The distance from the top of the cliff to the boat is 36 more than twice the height of the cliff, we denote this as \(c = 2b + 36\).

Step 3 ：We can use the Pythagorean theorem to solve for the height of the cliff (b). The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be written as: \(a² + b² = c²\).

Step 4 ：Substitute the given values into the Pythagorean theorem, we get \(144² + b² = (2b + 36)²\).

Step 5 ：Solving the equation, we get \(b = 290.2\).

Step 6 ：Final Answer: The height of the cliff is approximately \(\boxed{290.2}\) feet.