Hello! I am just wondering the steps to solve this equation?

Given sin α = n/m where n = 12 inches and m = 16 inches, solve for α to the nearest degree.

So it would be Sin(a) = 12/16, however, I'm unsure on how to solve for the degree a. Any help is appreciated!

there is no direct calculation solution (it's an infinite series)

use a calculator ... sin^-1 or arcsin

or a table

12/16 = 3/4 = .75 ... remember, sine is positive in Quad I and II

Got it! Thank you so much for your help!

To solve for α, the first step is to take the inverse sine (also known as arcsine) of both sides of the equation. This will allow us to isolate α.

The inverse sine function "arcsin" is denoted as sin^(-1) or asin. So the equation becomes:

arcsin(sin α) = arcsin(n/m)

Now, applying the arcsin function to both sides of the equation, we have:

α = arcsin(n/m)

Since n = 12 and m = 16, we substitute these values into the equation:

α = arcsin(12/16)

Next, we need to evaluate the arcsin(12/16). This can be done using a scientific calculator or a trigonometric table.

Calculating arcsin(12/16) will give the result in radians. However, since you want the answer in degrees, we need to convert radians to degrees by multiplying the result by (180/π).

So the final step is to multiply the result of arcsin(12/16) by (180/π) to obtain the angle α in degrees.