Answer:
14.9 miles
Explanation:
In the image below, the side of the triangle a, represents; "Peter leaves work and drives 10miles due south".
The side of the triangle b represents; "he then heads east for 11 miles to reach his home"
The distance between his work and home is represented by side c of the triangle.
This is a tight angle triangle, hence pythagoras theorem would be applied in solving it.
This theorem states that the square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides;
This means we have;
c² = a² + b²
c² = 10² + 11²
c = √(100+121)
c = 14.87
Rounding off to the nearest tenths = 14.9