Question

1. analyze and persevere a dog running an agility course has difficulty making turns. the sharper the angle, the more difficult the turn. which corner is most difficult for her to turn? image of a triangle with sides labeled: bc = 110 ft, ca = 90 ft, ab = 100 ft, and vertices labeled a, b, c

Explanation:

To determine the sharpest angle (most difficult turn), we use the relationship in a triangle: the smallest side is opposite the smallest angle, and the largest side is opposite the largest angle. The sides of the triangle (the outer agility course sides) are \( 90 \, \text{ft} \) (opposite angle \( B \)), \( 100 \, \text{ft} \) (opposite angle \( C \)), and \( 110 \, \text{ft} \) (opposite angle \( A \)).

Step 1: Identify the side lengths opposite each angle

• Side opposite angle \( A \): \( 110 \, \text{ft} \)
• Side opposite angle \( B \): \( 90 \, \text{ft} \)
• Side opposite angle \( C \): \( 100 \, \text{ft} \)

Step 2: Relate side length to angle measure

In a triangle, the smaller the side length, the smaller (sharper) the angle opposite it. The smallest side is \( 90 \, \text{ft} \), which is opposite angle \( B \). A sharper angle means a more difficult turn.

Answer:

The most difficult corner to turn is corner \( B \).