T.8 checkpoint: Applications of the Pythagorean theorem owt Isaac is mountain climbing with Rina and has just climbed a 6.2 -meter vertical rock face. Rina is standing at the bottom of the cliff, looking up at Isaac on a diagonal. If Rina is 10 meters away from Isaac, how far away from the cliff is Rina standing? If negessary, round your answer to the nearest tenth. meters

To find out how far Rina is standing from the cliff, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal line of sight from Rina to Isaac) is equal to the sum of the squares of the lengths of the other two sides (the height of the cliff and the distance from Rina to the base of the cliff). Here, we can set it up as follows: Let \( c \) be the length from Rina to Isaac (10 meters), \( a \) be the height of the cliff (6.2 meters), and \( b \) be the distance from Rina to the cliff. According to the theorem: \[ 10^2 = 6.2^2 + b^2 \] \[ 100 = 38.44 + b^2 \] \[ b^2 = 100 - 38.44 = 61.56 \] Now, take the square root: \[ b = \sqrt{61.56} \approx 7.85 \] Rounding to the nearest tenth gives approximately 7.9 meters. So, Rina is about 7.9 meters away from the cliff!