Question

annie likes to skate at a movie theater that is due south of her school and due west of her favorite game store. if the movie theater is 4 miles from her school and the straight - line distance between the school and the game store is 5 miles, how far is the movie theater from the game store?
square miles

Explanation:

Step1: Identify right triangle sides

Let:

• School to movie theater: $a = 4$ miles
• School to game store: $c = 5$ miles (hypotenuse)
• Movie theater to game store: $b$ (unknown leg)

Step2: Apply Pythagorean theorem

$$a^2 + b^2 = c^2$$
Substitute known values:
$$4^2 + b^2 = 5^2$$

Step3: Calculate squared values

$$16 + b^2 = 25$$

Step4: Solve for $b^2$

$$b^2 = 25 - 16 = 9$$

Step5: Solve for $b$

$$b = \sqrt{9} = 3$$

Answer:

3 miles