Question

1. use the pythagorean theorem to find the missing side length, x. a 11.8 km b 16.1 km c 22.0 km d 32.4 km 5. a baseball \diamond\ is a square with sides of 90 feet. how far will the ball have to be thrown from first base to reach third base? a the distance from first base to third base is 127.3 feet. b the distance from first base to third base is 180 feet. c the distance from first base to third base is 90 feet. d the distance from first base to third base is 135 feet. 6. what is the total measurement of all interior angles of a triangle? a 45 degrees b 90 degrees c 180 degrees d 360 degrees

Explanation:

4.

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. In this case, $c = 14$ km and $a = 8$ km, and we want to find $b=x$. So, $x=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 8$ and $c = 14$ into the formula: $x=\sqrt{14^{2}-8^{2}}=\sqrt{196 - 64}=\sqrt{132}\approx11.5$ km.

Step1: Recognize the shape and use Pythagorean theorem

A baseball diamond is a square. The distance from first base to third base is the length of the diagonal of the square. For a square of side length $s$, using the Pythagorean theorem $d^{2}=s^{2}+s^{2}$ (where $d$ is the diagonal length). Here, $s = 90$ ft, so $d=\sqrt{90^{2}+90^{2}}=\sqrt{8100 + 8100}=\sqrt{16200}\approx127.3$ ft.

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of any triangle is a well - known geometric fact. The sum of the interior angles of a triangle is always $180^{\circ}$.

Answer:

A. $11.5$ km

5.