If I know all 3 angles of a right triangle and the hypotenuse how do I figure out the short side length of the triangle?
pick one of the acute angles. Call it t. Label the opposite side x, and the hypotenuse h.
Then sin(t) = x/h
Do the same for the other angle and side, or use the Pythagorean Theorem to find the other side.
thank you
To find the short side length of a right triangle, you can use the trigonometric ratios sine, cosine, or tangent.
Let's assume you know the following information:
- The three angles of the right triangle are A, B, and C.
- The hypotenuse of the triangle is H.
To find the short side length, follow these steps:
1. Identify the angle that relates to the side length you want to find. Typically, the angles A and B are used with the side lengths opposite them, and angle C is used with the hypotenuse.
2. Determine which trigonometric function to use based on the relationship between the angle you identified and the side length you want to find:
- If you want to find the length opposite to an angle, use sine (sin)
- If you want to find the length adjacent to an angle, use cosine (cos)
- If you want to find the length and you have the angle and the hypotenuse, use tangent (tan)
3. Write down the formula for the trigonometric ratio you chose. For example:
- Sine (sin): sin(A) = opposite / hypotenuse
- Cosine (cos): cos(A) = adjacent / hypotenuse
- Tangent (tan): tan(A) = opposite / adjacent
4. Rearrange the formula to solve for the side length you want to find. For example:
- Sine (sin): opposite = sin(A) * hypotenuse
- Cosine (cos): adjacent = cos(A) * hypotenuse
- Tangent (tan): opposite = tan(A) * adjacent
5. Substitute the known values into the formula and calculate the result.
Remember to use the appropriate trigonometric ratio based on the relationship between the angle and side length you are interested in.