Question

three baseball players are playing catch. celine is directly south of bella and directly west of lindsey. celine and lindsey are 6 meters apart and lindsey and bella are 10 meters apart. how far apart are celine and bella? meters

Explanation:

Step1: Identify Triangle Type

Celine, Bella, Lindsey form a right triangle (Celine south of Bella, west of Lindsey: right angle at Celine). Let \( CB = x \) (distance between Celine and Bella), \( CL = 6 \) (Celine - Lindsey), \( BL = 10 \) (Bella - Lindsey).

Step2: Apply Pythagorean Theorem

In right triangle \( \triangle CBL \), \( BL^2 = CB^2 + CL^2 \). Substitute values: \( 10^2 = x^2 + 6^2 \).

Step3: Solve for \( x \)

\( 100 = x^2 + 36 \) → \( x^2 = 100 - 36 = 64 \) → \( x = \sqrt{64} = 8 \).

Answer:

8