- 1). Label one of the two unknown angles as "X." Note that one of the three angles in a right triangle is always known, and the size of that angle is 90 degrees. The 90-degree angle should never be labeled as X.
- 2). Label the longest side of the triangle as "H." This is the side positioned opposite to the right- or 90-degree angle of the triangle.
- 3). Label the side opposite the angle X as "O."
- 4). Label the side adjacent to angle X as "A." Note that side H (the hypotenuse) is also adjacent to angle X, but has already been labeled.
- 5). Calculate the angle X using the trigonometric relationships for right triangles. X is given by the formula: X = arctan (O/A) = arcsin (O/H) = arccos (A/H). For example, a right-angled triangle with H = 5 cm, O = 4 cm, and A = 3 cm has an angle X (the angle between sides H and A) = arctan (O/A), which equals arctan (4 cm/3 cm) = 53.1 degrees. Alternatively, X = arcsin (O/H), which equals arcsin (4 cm/5 cm) = 53.1 degrees. X can also be calculated using X = arccos (A/H), which equals arccos (3 cm/5 cm) = 53.1 degrees.
- 6). Repeat steps 1 to 5 to find the other unknown angle in the triangle.
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