Given a right triangle, solve for θ

To solve for θ in a right triangle, you need to know at least two sides of the triangle. The three sides are typically referred to as the opposite (O), adjacent (A), and hypotenuse (H).

Here are the steps:

1. Identify the two sides that you know in relation to the angle θ. These could be any two of the following: opposite (O), adjacent (A), or hypotenuse (H).

2. Depending on which two sides you know, you can use one of the following trigonometric ratios to solve for θ:

   • Sine (sin) = O/H
   • Cosine (cos) = A/H
   • Tangent (tan) = O/A

3. Rearrange the equation to solve for θ. This will involve using the inverse function (sin^-1, cos^-1, or tan^-1) on your calculator.

For example, if you know the opposite and hypotenuse sides and you're using the sine ratio, the equation would be:

sin(θ) = O/H

To solve for θ, you would rearrange this to:

θ = sin^-1(O/H)

4. Substitute the values of the sides into the equation and calculate θ.

Remember, the answer will be in radians if your calculator is in radian mode, and in degrees if it's in degree mode.