Question

mrs. lambert is teaching a 5th grade class. she is standing 6 meters in front of lacey. brendan is sitting to lacey’s right. if brendan and mrs. lambert are 10 meters apart, how far apart are lacey and brendan? meters

Explanation:

Step1: Identify the triangle type

The positions form a right triangle, with Mrs. Lambert - Lacey distance (6m) as one leg, Lacey - Brendan distance (let's call it \( x \)) as another leg, and Mrs. Lambert - Brendan distance (10m) as the hypotenuse.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse, and \( a, b \) are the legs. Here, \( a = 6 \), \( c = 10 \), so we solve for \( b \) (which is \( x \)):

$$ x^2 + 6^2 = 10^2 $$

$$ x^2 + 36 = 100 $$

$$ x^2 = 100 - 36 $$

$$ x^2 = 64 $$

$$ x = \sqrt{64} = 8 $$

Answer:

8