Question

erics work
line 1: ( 5 ^ { 2 } + x ^ { 2 } = 12 ^ { 2 } )
line 2: ( 25 + x ^ { 2 } = 144 )
line 3: ( sqrt { x ^ { 2 } } = sqrt { 119 } )
line 4: ( x = 10 - 11 ) miles
a drone took off from the ground and flew 12 miles vertically, then 5 miles east. at that point, what was the straight - line distance of the drone from its starting point?
erics work for this problem is shown. did he solve it correctly? if not, explain his mistake.
eric is incorrect. he made a mistake in line 4, because ( sqrt { 119 } = 59.5 ).
eric is incorrect. in his sketch, the length of the vertical leg should be 12 miles and the hypotenuse should be the unknown distance.

Explanation:

Step1: Identify Pythagorean theorem parts

The drone's path forms a right triangle: vertical leg = 5 miles, horizontal leg = 12 miles, hypotenuse = straight-line distance $x$. Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Correct formula setup

$5^2 + 12^2 = x^2$ (hypotenuse is unknown, so it should be isolated as $x^2$).

Step3: Calculate squares

$25 + 144 = x^2$ → $169 = x^2$.

Step4: Solve for x

$x = \sqrt{169} = 13$ miles. Eric mixed up legs/hypotenuse in his sketch (labeled hypotenuse as 12 instead of unknown).

Answer:

Eric is incorrect. In his sketch, the length of the vertical leg should be 5 miles and the hypotenuse should be the unknown distance. The correct straight-line distance is 13 miles.