Question

The bottom end of a ramp at a warehouse is 10 feet from the base of the main dock and is 11 feet long. How high is the dock? Write your answer as a decimal rounded to the nearest tenth.

Answer 1

The height of the dock is approximately 5.2 feet.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). In this case, the ramp, the dock, and the ground form a right triangle, where the ramp is one leg, the height of the dock is the other leg, and the distance between the ramp and the dock is the hypotenuse.

Using the Pythagorean theorem, we have:

$c^2 = a^2 + b^2$

where c is the hypotenuse (11 feet), a is the distance from the ramp to the base of the dock (10 feet), and b is the height of the dock (what we want to find).

Rearranging the equation, we have:

$b^2 = c^2 - a^2$

$b = √(11^2 - 10^2)$

b ≈ 5.2 feet (rounded to the nearest tenth)

Therefore, the height of the dock is approximately 5.2 feet.

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Answer 2

The height of the dock is approximately 4.6 feet.

• The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the legs of a right triangle, can be used to solve this issue. In this instance, the dock serves as the right triangle's vertical leg, the ramp serves as its horizontal leg, and the length of the ramp serves as the hypotenuse.

• Let x represent the dock's height. Next, we have

• x^2 + 10^2 = 11^2

• When we simplify this equation, we obtain:

• x^2 = 11^2 - 10^2
• x^2 = 121 - 100
• x^2 = 21

• When we square the two sides, we obtain:

• x = sqrt(21)

• We may use a calculator to get the value of x to the closest tenth as follows:

• x ≈ 4.6

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