In baseball, the lengths of the paths between consecutive...

Name: Problem 29, Chapter 9: Geometry A Common Core Curriculum
Uploaded: 2019-11-07T23:20:04-08:00
Duration: 5 min 11 s
Channel: Steven Swee
Description: In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out?

In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out?

Key Concepts

Properties of a Square

A square is a quadrilateral with all sides equal and every angle measuring 90 degrees. Understanding the properties of a square enables the use of the Pythagorean Theorem to find the length of its diagonal. The diagonal forms the hypotenuse of a right triangle with the sides of the square as the other two legs, providing a clear application of these geometrical principles.

Right Triangle

A right triangle is a triangle with one 90-degree angle. In geometric problems involving perpendicular paths or edges, such as the ones seen in a square configuration, a right triangle is often formed. This concept is essential because it lays the foundation for applying further mathematical principles, like the Pythagorean Theorem, to determine unknown side lengths.

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in geometry that relates the lengths of the sides in a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is widely used to compute diagonal distances and is crucial when only the lengths of the perpendicular sides are known.

Transcript

00:01 So for this problem, we have a baseball field.

00:03 And you know what a baseball field looks like? you could recognize this as the baseball diamond, right? technically, it's a wrong base because the distance between each consecutive base is 90 feet.

00:18 So, oh, it's really a square because the angles between the bases here, when you make a turn, is, from one base to another, is 90 degrees.

00:28 So it's really a tilted square.

00:32 You can think of it like that.

00:34 But for this scenario here, we have a player here, my little baseman, or my, i guess, baseball player.

00:44 And he's trying to steal first base here, right, first base.

00:49 He's trying to get a steal to get for first base to second base here.

00:52 So he wants to get from here to here.

00:55 Now, the thing is, right, the steel happens when i have my guy at the pitcher's mount here, right? he throws the ball and it's caught by the catcher here.

01:10 And the catcher has to throw the ball all the way up here or home plate to second base.

01:16 He's there.

01:18 And we're asked how far does the ball have to travel? so if he goes home base here, this is home base.

01:25 All the way to second base there.

01:28 And if i were to label the distance of the ball has to travel, it would be this distance here.

01:37 I'll call that distance d.

01:40 D for distance.

01:43 So how do we do this? now, the thing is, because we know that each distance between two consecutive bases, so home plate to first base and first base, the second base, is 90 feet, and we know that to get from one base to another here, you have to go in the direction of 90 degrees.

02:06 We can actually set up a right triangle for this.

02:10 Do we see it? so from home to first base here, let me write this as home.

02:19 Home to first base is in this direction, and it's 90 feet...

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