Question

for each problem below. theorem to solve for the indicated value.

1. alejandra walked 3km east and 4km north. calculate how far she is from her starting point.
2. hectors back yard is on a corner lot and is triangular in shape. if the short side of his yard is 12m, the long side is 15m how long is the third side of his yard?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 3\) (east - ward distance), \(b=4\) (north - ward distance), and \(c\) is the distance from the starting point.
Substitute \(a = 3\) and \(b = 4\) into the formula: \(3^{2}+4^{2}=c^{2}\).

Step2: Calculate the squares

\(3^{2}=9\) and \(4^{2}=16\). So, \(9 + 16=c^{2}\).

Step3: Sum and find the square root

\(9+16 = 25\), then \(c=\sqrt{25}\).

Answer:

\(5\) km