#1) 5.8 miles #2) 9.8 ft #3) 56 in #4) 5.2 #5) 13 #6) 5.4 ft
For #1, we have the two legs of the triangle and must find the hypotenuse. Using the Pythagorean theorem, we have: 3²+5²=x² 9+25=x² 34=x² √34 = x ≈ 5.8 mi
For #2, we have one leg and the hypotenuse: x²+2²=10² x²+4=100
Subtract 4 from both sides: x²=96
Take the square root of both sides: x=√96≈9.8 ft
For #3, we have one leg and the hypotenuse: x²+42²=70² x²+1764=4900
Subtract 1764 from both sides: x²=3136
Take the square root: x=√3136=56 in
For #4, the height splits the base into half; we have one leg and the hypotenuse: x²+3²=6² x²+9=36
Subtract 9 from both sides: x²=27
Take the square root: x=√27 = 5.2
For #5, we have both legs: 5²+12²=x² 25+144=x² 169=x²
