Isaiah walks 3 miles due north, turns and then 5 miles due east. How far is he from his starting point? A 10-foot ladder is leaning against a wall. The base of the ladder is 2 feet from the base of the building. How far up the building does the ladder fall? A television is measured by its diagonal. If the height of a 70 inch television is 42 inches, what is the width? An equilateral triangle has a side length of 6. What is the height of the triangle? A right triangle has a height of 12 and a width of 5. How long is the diagonal? A string is tied to the top of a plant to keep it stabilized. The plant is 5 feet tall and the string is connected to the ground 2 feet from the base of the plant. How long is the string?Answers from the box 135.25.45.89.856

#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

Take the square root:
x=√169=13

For #6, we have both legs:
5²+2²=x²
25+4=x²
29=x²

Take the square root:
x=√29 = 5.4 ft