Pre-cal Problem, please, help is very much appreciated!

Let y be the length of the third side. By the Pythagorean theorem,

y² + x² = 3² = 9

so that

y = √(9 - x²)

(taking the positive root because one expects length to be positive)

Then by the definitions of sine, cosine, and tangent, we have

sin(θ) = x / 3   →   θ = sin⁻¹(x / 3)

cos(θ) = √(9 - x²) / 3   →   θ = cos⁻¹(√(9 - x²) / 3)

tan(θ) = x / √(9 - x²)   →   θ = tan⁻¹(x / √(9 - x²))

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.