Answer:
9. 6.6
10. 6
11. 8.9
Step-by-step explanation:
Pythagorean theorem states that a^2 + b^2 = c^2 where a and b are legs, and c is the hypotenuse (the longest side of the triangle).
For the first one, you're given the leg (3.1 in) and the eg (5.8 in), so you can substitute those into the equation:
a^2 + b^2 = c^2
(3.1)^2 + (5.8)^2 = c^2
Then simplify
9.61 + 33.64 = c^2
43.25 = c^2
To isolate c, take the square root of both sides.
The square root of 43.25 is 6.57647322, but they want you to round it to the nearest tenth, so round it to 6.6
For the second one, you're given one leg length and the hypotenuse.
8^2 + b^2 = 10^2
64 + b^2 = 100
To solve for b, subtract 64 from both sides
b^2 = 36
and take the square root of both sides
b = 6
For the last one, you're given a leg length and the hypotenuse
a^2 + 4.3^2 = 9.9^2
a^2 + 18.49 = 98.01
to isolate a, subtract 18.49 from both sides
a^2 = 79.52
then take the square root of both sides
a = 8.91739872 which rounds to 8.9
