Question

a cyclist rides 30 miles due east and then 40 miles due north. to the nearest mile, how far is the cyclist from the starting point? 70 miles 60 miles 50 miles

Explanation:

Step1: Identify right triangle sides

The cyclist's path forms a right triangle with legs $a=30$ miles and $b=40$ miles. We need to find the hypotenuse $c$.

Step2: Apply Pythagorean theorem

Use the formula $c = \sqrt{a^2 + b^2}$
$$c = \sqrt{30^2 + 40^2}$$

Step3: Calculate squared terms

$$c = \sqrt{900 + 1600}$$

Step4: Sum and compute square root

$$c = \sqrt{2500} = 50$$

Answer:

50 miles