Question

"a man drove 10 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. if a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?"

Answer 1

Answer:

11.2 miles

Step-by-step explanation:

We can create a triangle from the information given.

We can call the starting point (0,0) in the coordinate system.

• 10 mi east - 10 miles to the right. then,
• 5 mi north - 5 miles above

See the attached picture. The direct distance is labeled as x.

Now we need to find x using pythagorean theorem.

Pythagorean Theorem = leg²+leg²=hypotenuse²

Solving for x:

$10^2+5^2=x^2\\100+25=x^2\\125=x^2\\x=\sqrt{125}\\x=11.18$

Rounding to nearest tenth, we have 11.2 miles

Answer 2

This problem can be directly solved using the hypotenuse formula. Taking 10 mi and 5 mi as the two sides of the triangle, we find for the hypotenuse (distance directly from his home to his place of work):

c^2 = 10^2 + 5^2

c^2 = 100 + 25

c = 11.18 m

c = 11.2 meters