A bike ramp is built in the shape of a right triangle. The base beam has a length of 18.2 m, and the ramp has a height of 11.65 m. What is the length of the ramp surface to the nearest tenth of a meter? Describe in detail

To find the length of the ramp surface, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the base beam represents one of the sides of the right triangle, with a length of 18.2 m, and the height of the ramp represents the other side, with a length of 11.65 m. Let's designate the length of the hypotenuse (ramp surface) as "c".

According to the Pythagorean theorem:
c² = a² + b²

Where:
a = 18.2 m (base beam)
b = 11.65 m (height of the ramp)

Substitute the values into the equation:
c² = 18.2² + 11.65²
c² = 331.24 + 135.7225
c² = 466.9625

Now, calculate the square root of both sides to find the length of the ramp surface:
c = √466.9625
c ≈ 21.6 m

Therefore, the length of the ramp surface to the nearest tenth of a meter is approximately 21.6 meters.