Final answer:
To find side lengths of a right triangle, use the Pythagorean theorem or trigonometric functions based on the given side lengths and angles. After substituting the known values, verify that the results are reasonable and correspond with the geometry of the triangle. Scale factors, if provided, are used to find actual lengths from a scaled drawing.
Step-by-step explanation:
To find the exact values of the side lengths of a right triangle, we often employ the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): a² + b² = c². If you are given one side and one angle, you can use trigonometric functions like sine, cosine, and tangent that relate the angles of a right triangle to its side lengths. For example, the cosine of an angle (θ) in a right triangle is equal to the length of the adjacent side (x) divided by the hypotenuse (h): cos(θ) = x/h, and the sine is the opposite side (y) divided by the hypotenuse: sin(θ) = y/h. When you substitute the known values into these equations and solve for the unknowns, you can obtain the lengths of the missing sides.
To ensure that the answer is reasonable, always check if the computed side lengths make sense with the given measurements of the triangle. The side lengths should correspond correctly with the angles, and the longest side should always be the hypotenuse in a right triangle. If you have an angle in radians, make sure to use it as such in your calculations.
If using scale factors for the triangle, such as scale/actual=1/20 or scale/actual=1/5.5, this represents a ratio used to find the actual length of the sides when given a scaled drawing. To find the actual lengths, multiply the scale lengths by the scale factor.