Find all missing sides and angles with work

Brainliest pls?

Side BC = sqrt 80 or 8.94

Angle A = 48.19 degrees

Angle C = 41.81

Step-by-step explanation:

Using the Pythagorean Theorem, we can solve for the missing side, BC:

a^2 + b^2 = c^2 (Substitute)

8^2 + b^2 = 12^2 (Simplify)

64 + b^2 = 144 (Subtract 64 from both sides)

b^2 = 80

b = sqrt (80)

b is approximately equal to 9 and when rounded to the hundredths, it is equal to 8.94.

Now that we know the sides, we can use trig relationships between the sides to find the angles:

sin A = (sqrt 80)/12 (Using the square root directly will result in accurate answers  |  take the inverse sine of both sides)

A = sin-1 ((sqrt 80)/12)

Angle A = 48.19 degrees (approximation to the nearest hundredth)

We know that B is a right angle, hence 90 degrees.

sin C = 8/12 (Take the inverse sine of both sides)

C = sin-1 (8/12)

Angle C = 41.81 degrees (approximation to the nearest hundredth)