Jack is mountain climbing with Liz and has just climbed a 16-meter vertical rock face. Liz is standing 12 meters away from the bottom of the cliff, looking up at Jack. How far away are Jack and Liz? (Hint: use Pythagorean Theorem a^2 + b^2 = c^2) *1 point20 meters28 meters400 meters8 meters

Answer 1

To find the distance between Jack and Liz, we can use the Pythagorean theorem. The vertical height of the rock face (16 meters) and the horizontal distance from Liz to the bottom of the cliff (12 meters) form a right triangle, with the distance between Jack and Liz being the hypotenuse.

Let:

• \( a = 16 \) meters (the height of the rock face)
• \( b = 12 \) meters (the horizontal distance)

According to the Pythagorean theorem: \[ c^2 = a^2 + b^2 \]

Substituting the values: \[ c^2 = (16)^2 + (12)^2 \] \[ c^2 = 256 + 144 \] \[ c^2 = 400 \] \[ c = \sqrt{400} = 20 \]

So, the distance between Jack and Liz is 20 meters.