Becky likes to skate at a movie theater that is due south of her school and west of her favorite ice cream parlor. If the movie theater is 4 miles from her school and the straight-line distance between the school and the I cream parlor is 5 miles, how far is the movie theater from the ice cream parlor

The movie theater is 3 miles away from the the ice cream parlor.

Step-by-step explanation:

The position of Becky's school (S) and the movie theater (M) and the ice cream parlor (I) make a right triangle.

Hence, Δ SMI is a right triangle with ∠ M is the right angle i. e. 90°.

Now, given length of segment SM is 4 miles and the hypotenuse i. e. line segment SI = 5 miles.

Hence, applying Pythagoras Theorem,

SI² = SM² + MI²

⇒ 5² = 4² + MI²

⇒ MI = 3 miles.

Therefore, the movie theater is 3 miles away from the ice cream parlor. (Answer)