Question

1. a man leaves work and walks 2 miles west and 1.5 miles south to get home. how far is his work from his home? (draw a picture!)

○3.5 mi
○2.5 mi
○1.3 mi
○2.8 mi

Explanation:

Step1: Identify right triangle sides

The west and south paths form legs of a right triangle: $a=2$ mi, $b=1.5$ mi.

Step2: Apply Pythagorean theorem

Use $c=\sqrt{a^2 + b^2}$ to find the straight-line distance.

$$ c=\sqrt{2^2 + 1.5^2} $$

Step3: Calculate squared terms

Compute $2^2=4$ and $1.5^2=2.25$.

$$ c=\sqrt{4 + 2.25} $$

Step4: Sum and take square root

Add terms, then find the square root: $\sqrt{6.25}=2.5$.

$$ c=2.5 $$

Answer:

2.5 mi