Question

seths house is due west of bloomington and due south of hampton. bloomington is 7 miles from seths house and 10 miles from hampton. how far is hampton from seths house, measured in a straight line? if necessary, round to the nearest tenth.

Explanation:

Step1: Identify right triangle sides

Let Seth's house = S, Bloomington = B, Hampton = H. SB=7 (leg), BH=10 (hypotenuse), SH=? (other leg).

Step2: Apply Pythagorean theorem

$SH = \sqrt{BH^2 - SB^2} = \sqrt{10^2 - 7^2}$

Step3: Calculate value

$\sqrt{100 - 49} = \sqrt{51} \approx 7.1$

Answer:

7.1