Question

finding an unknown side length in a right triangle
part e: finding the hypotenuse of a right triangle
sketch of note 1
note
side length a
side length b
pythagorean theorem: (a^2 + b^2 = c^2)
hypotenuse c ((sqrt{c^2} = c))
1
2
3
4

Explanation:

Step1: Identify the sides

From the table, for Hole 1, side \( a = 3 \), side \( b = 4 \).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \( a^2 + b^2 = c^2 \). Substitute \( a = 3 \) and \( b = 4 \): \( 3^2 + 4^2 = c^2 \). Calculate \( 3^2 = 9 \), \( 4^2 = 16 \), so \( 9 + 16 = c^2 \), \( 25 = c^2 \).

Step3: Solve for \( c \)

Take the square root of both sides: \( c = \sqrt{25} = 5 \).

Answer:

For Hole 1, the hypotenuse \( c = 5 \)