a ≈ 9.4, b ≈ 12.0
Step-by-step explanation:
Using Pythagoras' identity in the right triangles.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
a² = 8² + 5² = 64 + 25 = 89 ( take the square root of both sides )
a = ≈ 9.4 ( to 1 dec. place )
b² + 12² = 17²
b² + 144 = 289 ( subtract 144 from both sides )
b² = 145 ( take the square root of both sides )
b = ≈ 12.0 ( to 1 dec. place )