Math Problem Statement

How long is the base, round to 2 decimal points and don't round until you get the answer

Solution

To solve the problem and find the length of the base of the ramp, we can apply the Pythagorean theorem. The problem involves a right triangle where:

  • The hypotenuse (cc) is 2.2 meters,
  • The height (aa) is 0.35 meters,
  • The base (bb) is what we're trying to find.

According to the Pythagorean theorem:

c2=a2+b2c^2 = a^2 + b^2

Substituting the given values:

2.22=0.352+b22.2^2 = 0.35^2 + b^2

Now, let's solve for bb:

b2=2.220.352b^2 = 2.2^2 - 0.35^2

b=2.220.352b = \sqrt{2.2^2 - 0.35^2}

I'll calculate this to give you the precise length of the base rounded to two decimal points.The length of the base of the ramp is approximately 2.17 meters when rounded to two decimal points.

Would you like more details or have any questions about this calculation?

Here are some related questions you might find interesting:

  1. How do you calculate the angle of elevation of the ramp?
  2. What would be the base length if the height were increased to 0.5 meters?
  3. How does changing the hypotenuse affect the base and height of a right triangle?
  4. Can the Pythagorean theorem be applied in non-Euclidean geometry?
  5. What is the relationship between the area of a right triangle and its base and height?

Tip: When working with the Pythagorean theorem, ensure that all measurements are in the same units before performing any calculations.

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Math Problem Analysis

Mathematical Concepts

Pythagorean theorem
Right triangle
Square root

Formulas

Pythagorean theorem: c^2 = a^2 + b^2
Square root: b = sqrt(c^2 - a^2)

Theorems

Pythagorean theorem

Suitable Grade Level

High School