PLEASE HELP With 9, 10 and 11

9. 6.6

10. 6

11. 8.9

Step-by-step explanation:

Pythagorean theorem states that a^2 + b^2 = c^2 where a is the length, b is the base, and c is the hypotenuse (the longest side of the triangle).

For the first one, you're given the length (3.1 in) and the base (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 the base and 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

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