Question

use pythagorean theorem to answer the following question.
andrew walks his sister to school every day. they walk 1.2 miles south, and then 0.35 miles west to get to school. approximately how far are they from home if they could have walked diagonally to get there?
round the answer to two decimal places.
miles from home

Explanation:

Step1: Identify the right triangle sides

The south and west walks form the legs of a right triangle. Let \( a = 1.2 \) (south), \( b = 0.35 \) (west).

Step2: Apply Pythagorean Theorem

The Pythagorean Theorem is \( c=\sqrt{a^{2}+b^{2}} \). Substitute \( a = 1.2 \) and \( b = 0.35 \):
\( a^{2}=1.2^{2}=1.44 \), \( b^{2}=0.35^{2}=0.1225 \).
Sum: \( 1.44 + 0.1225 = 1.5625 \).
Then \( c=\sqrt{1.5625} \approx 1.25 \) (wait, no, wait: \( 1.2^2 = 1.44 \), \( 0.35^2 = 0.1225 \), sum is \( 1.44 + 0.1225 = 1.5625 \)? Wait, no, \( 1.2^2 = 1.44 \), \( 0.35^2 = 0.1225 \), sum is \( 1.44 + 0.1225 = 1.5625 \)? Wait, no, \( 1.2\times1.2 = 1.44 \), \( 0.35\times0.35 = 0.1225 \), adding them: \( 1.44 + 0.1225 = 1.5625 \). Then square root of \( 1.5625 \) is \( 1.25 \)? Wait, no, \( 1.25^2 = 1.5625 \). Wait, but let's recalculate:

Wait, maybe I made a mistake. Wait, \( 1.2^2 = 1.44 \), \( 0.35^2 = 0.1225 \), sum is \( 1.44 + 0.1225 = 1.5625 \). Then \( \sqrt{1.5625} = 1.25 \). Wait, but let's check again. Wait, 1.2 miles south and 0.35 miles west. So the right triangle has legs 1.2 and 0.35. So hypotenuse \( c = \sqrt{1.2^2 + 0.35^2} \).

Calculating \( 1.2^2 = 1.44 \), \( 0.35^2 = 0.1225 \), sum is \( 1.44 + 0.1225 = 1.5625 \). Then square root of 1.5625 is 1.25. Wait, that's exact? But let's confirm: 1.25 squared is (1 + 0.25)^2 = 1 + 0.5 + 0.0625 = 1.5625. Yes. So the distance is 1.25 miles? Wait, but maybe I miscalculated the sum. Wait, 1.44 + 0.1225: 1.44 + 0.1 = 1.54, 1.54 + 0.0225 = 1.5625. Yes. So square root of 1.5625 is 1.25. So the answer is 1.25 when rounded to two decimal places? Wait, but maybe the problem is different? Wait, no, 1.2 and 0.35. Let me check again.

Wait, maybe I misread the numbers. The problem says 1.2 miles south and 0.35 miles west. So legs are 1.2 and 0.35. So Pythagorean theorem: \( c = \sqrt{1.2^2 + 0.35^2} \). Calculating:

\( 1.2^2 = 1.44 \)

\( 0.35^2 = 0.1225 \)

Sum: \( 1.44 + 0.1225 = 1.5625 \)

Square root: \( \sqrt{1.5625} = 1.25 \)

So the distance is 1.25 miles.

Answer:

1.25