Question

Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town Hall.

Part A

What is the length of a straight line between the school and the fire station? Round to the nearest tenth.

Part B

The hospital is 3.1 miles west of the fire station. What is the length of a straight line between the school and the hospital? Round to the nearest tenth.

Answer 1

a. The length of a straight line between the school and the fire station is 4.6 miles

b. The length of a straight line between the school and the hospital is 2.1 miles

Explanation:

See attachment

Given.

Distance between the school and the town hall = 4.3 miles directly east

Distance between the fire station and the town hall = 1.7 miles directly north.

The length of a straight line between the school and the fire station is calculated by solving the length of hypotenuse of the right angled triangle (see attachment A)

Using Pythagoras theorem;

x² = 1.7² + 4.3²

x² = 2.89 + 18.49

x² = 21.38 --- Take square roots

x = 4.6 miles

The length of a straight line between the school and the fire station is 4.6 miles

b.

The length of a straight line between the school and the hospital is calculated by solving the length of hypotenuse of the right angled triangle (see attachment B)

Using Pythagoras theorem;

x² = 1.7² + 1.2²

x² = 2.89 + 1.44

x² = 4.33 --- Take square roots

x = 2.1 miles

The length of a straight line between the school and the hospital is 2.1 miles